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   "source": [
    "<!--BOOK_INFORMATION-->\n",
    "<img align=\"left\" style=\"padding-right:10px;\" src=\"images/book_cover.jpg\" width=\"120\">\n",
    "\n",
    "*This notebook contains an excerpt from the [Python Programming and Numerical Methods - A Guide for Engineers and Scientists](https://www.elsevier.com/books/python-programming-and-numerical-methods/kong/978-0-12-819549-9), the content is also available at [Berkeley Python Numerical Methods](https://pythonnumericalmethods.berkeley.edu/notebooks/Index.html).*\n",
    "\n",
    "*The copyright of the book belongs to Elsevier. We also have this interactive book online for a better learning experience. The code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work on [Elsevier](https://www.elsevier.com/books/python-programming-and-numerical-methods/kong/978-0-12-819549-9) or [Amazon](https://www.amazon.com/Python-Programming-Numerical-Methods-Scientists/dp/0128195495/ref=sr_1_1?dchild=1&keywords=Python+Programming+and+Numerical+Methods+-+A+Guide+for+Engineers+and+Scientists&qid=1604761352&sr=8-1)!*"
   ]
  },
  {
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   "source": [
    "<!--NAVIGATION-->\n",
    "< [23.4 Numerical Error and Instability](chapter23.04-Numerical-Error-and-Instability.ipynb) | [Contents](Index.ipynb) | [23.6 Summary and Problems](chapter23.06-Summary-and-Problems.ipynb) >"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "# Python ODE Solvers (BVP)"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "In *scipy*, there are also a basic solver for solving the boundary value problems, that is the *scipy.integrate.solve_bvp* function. The function solves a first order system of ODEs subject to two-point boundary conditions. The function construction are shown below:\n",
    "\n",
    "**CONSTRUCTION:**  \n",
    "\n",
    "Let $F$ be a function object to the function that computes \n",
    "\n",
    "$$\\frac{dy}{dx} = F(t, S(t))$$\n",
    "$$S(t0)=S0$$\n",
    "\n",
    "$t$ is a one-dimensional independent variable (time), $S(t)$ is an n-dimensional vector-valued function (state), and the $F(t, S(t))$ defines the differential equations. $S0$ be an initial value for $S$. The function $F$ *must* have the form $dS = F(t, S)$, although the name does not have to be $F$. The goal is to find the $S(t)$ approximately satisfying the differential equations, given the initial value $S(t0)=S0$. \n",
    "\n",
    "The way we use the solver to solve the differential equation is: $$solve\\_ivp(fun, t\\_span, s0, method = 'RK45', t\\_eval=None)$$\n",
    "\n",
    "where $fun$ takes in the function in the right-hand side of the system. $t\\_span$ is the interval of integration $(t0, tf)$, where $t0$ is the start and $tf$ is the end of the interval. $s0$ is the initial state. There are a couple of methods that we can choose, the default is 'RK45', which is the explicit Runge-Kutta method of order 5(4). There are other methods you can use as well, see the end of this section for more information. $t\\_eval$ takes in the times at which to store the computed solution, and must be sorted and lie within $t\\_span$. \n",
    "\n",
    "Let's try one example below. "
   ]
  },
  {
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   "execution_count": null,
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   "outputs": [],
   "source": []
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   "outputs": [
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VmQ3+nl6zBMs0WaVlykNfrOCmdxf79oAY0qUVn/1pFMO6JlTT2wCcNLA9X9x4LIcnO/9eZQpPTVvFbVOWUFJa5nF0xhhjjCmXU1jCs9Mr9qS645S+7L9FX/2LDA/j5hN6+44f/zqVsrLQvhBrCZZpkvbkFXP5q3N5YdY637mzhnXi3auPol0TLWRRW51aNePtq47iz377Z0yZv4lr35xPflGph5EZY4wxptwLs9axM7cIgAkD2jG8W+OthTptSEf6tIsDYNmWvXy1bFujvbcXLMEyTc6ajBzOeO5H3xB1mMDdE/vxr3OHEBNp661qIyI8jJtP7MMzvxtKRJhzNWzaigz+MPkX9uQVexydMcYY07RlZBfw0mznonJ4mHDbhL6N+v7hYcItJ1aMYv3rm9SQnuliCZZpUhZt3M2Zz/1I2o5cAOJjInj1siO48tgejTJMHupOH9qJly4Z4SvlPm/9Ls57fg7b9hR4HJkxxhjTdD0zbTV57qyS80Z0ISWpRaPHcEL/dgzp0gqAtZm5fLRwc6PH0FgswTJNxsINu/jDS7+QXVACQEpSCz69YRSjeyd6HFloGdMnibeuOpKEWKf4Rer2bM7+z0+sy8yppqcxxhhj6tvazBzembsRgGaR4dw0vlc1PRqGiPDXCX18x09PW01hSWguJbAEyzQJCzbs4uLJv5Jd6CRXI7ol8NEfR5LctrnHkYWmw7om8P61R9OxpbOebfPufM757xyWbNpdTU9jjDHG1KfHv0ql1C0qceWx3UnycK35MSltGdmzDeB8N3jn142exdKQLMEyIW/++n2Tq8OTE3j18iOIi4n0OLLQlpIUx5TrRvqmIWTlFvH7F37mh9U7PI7MGGOMaRoWbNjlKyjRunkUV4/u4XFEcKvfKNb/+24NeUUlHkbTMCzBMiFt/vosLp78CzlucnVEcmteuewIWkRHeBxZ09CxVTPev+ZoDuvqzLnOLSrlsld/5fMlWzyOzBhjjAl95YUtAP48LiUgLi4P65rA+H7O/ls7cgp57af1HkdU/yzBMiFrXnoWF0/+lVx3UecR3VvzymWHW3LVyBKaR/G/K49kTB9nrVtxqfKntxfy1i8bPI7MGGOMCV178ouZtiIDgFaxkfz+yK4eR1Th1gkVFQXf/nUDqqG1L5YlWCYkzU3P4uKXK5KrI7u35tXLDqe5JVeeiI2K4MWLR3DmYZ0AUIW7Pv6NTxfbSJYxxhjTEL74bStFJU4p9FMHdyA6InC2ounbPp4jujv7cG3IymPBhtBao20Jlgk5v6ZlccnLv/rKkR7Vwxm5io2y5MpLkeFh/OvcIVxydDfASbJufncRM1MzPI7MGGOMCT0fLtjke3zmYZ09jKRqZwzt5Hv8yaLQKtluCZYJKb+s28mlr1QkV0f3aMMrlx5hyVWACAsT7j1tAGcNc/6olpQp1745n/nrszyOzBhjjAkdG7PymJu+C4DkNrEMc9dCB5JTBrUnMtzZg/TzJVspDqGNhy3BMiHDSa7m+pKrkT3b8PKlh9MsKnCGxI2TZD169mDG90sCoKC4jMtemcvKbXs9jswYY4wJDf6b+J55WGdExMNoqtYqNooxfZzvAlm5RSFVZdgSLBMSVm/P5srX55Ff7CRXo1LaMvkSS64CVWR4GP++YJhv/vXeghIunvwrG7PyPI7MGGOMCW6qWinB6nSQ1t7ynyb4cQhNE7QEywS9zOxCLnt1LtkFTin2kT3b8NIlIyy5CnAxkeG8dMkI+neIByAju5CLJv9CRnaBx5EZY4wxwWvRxt2k7cgFYES3BLq2ifU4ogM7vl+Sr7rzN8u2k1sYGntiWYJlglp+USlXvj6PTbvyAejbPo7n/zCcmEhLroJBfEwkr11+BMnuH//1O/O45OW57Mkv9jgyY4wxJjjtM3o1LHBHr8C52HrSwPYA5BeX8u3y7R5HVD88TbBEpIuITBGRPSKyV0Q+FJEaFekXka4i8pqIbBCRPBFZJSIPikjzho7bBIayMuWmdxexeKNT2jMxLprJlx4eEJvomZpLjIvmjSuOpF18NAArtu7lytfmku+upTPGGGNMzRSVlPGZuwVKVHgYpw7q6HFE1QvFaYKeJVgiEgt8B/QFLgH+APQCZlSXJLnPTwNGA38HJgIvAbcALzdg2CaAPPrVSr5atg2AZpHhvHzJ4XRq1czjqExtdGkdy+uXH0nLZk5yPDd9Fze8tSCkKgoZY4wxDW1maga78pxZIOP6JtEyNvAvOh/dsw1Jcc5F1tmrd7Ajp9DjiOrOyxGsq4AewBmq+rGqfgJMAroB11TT9xicZOwaVX1NVWeo6mPAM8DZbvJmQtj/flnP87PWASACz/7+MAZ1bulxVKYu+rSPc6o+utM7p6/M4K9TllBWFlq7uxtjjDENJZimB5YLDxMmDXFG2krLlKlLtnocUd15mWBNAn5W1TXlJ1Q1DfgROL2avlHufeW6zrtxfqbAq0Vp6s3M1Azu+WSZ7/jvE/tzQv92HkZk6svwbgn89w/DfftifLRwM09PW+VxVMYYY0zg25NXzPQVGQC0io1krFsCPRic4Vfp0D9JDFZeJlgDgKVVnF8G9K+m7zRgNfCoiPQXkRYiMg64EfivqubWb6gmUKzYupcb3lpIqTuqccnR3bjsmGRvgzL16rjeiTx53lDKt+x49rs1fLV0m7dBGWOMMQFu6m9bKXKn1p86uANREcFTy25Ax3h6JjorhBZt3E36juD+Ku/lv3xrYFcV57OAhIN1VNUCYBRO/MuAbGA68DlwQ22CEZH55bfa9DcNb/veAi5/dS45bgnP4/smcc9pAwJy8zxTN6cN6cjN43v7jm95bxGrt2d7GJEJVXUsthQjIo+LyFYRyReROSIyuop2YSJyh4iki0iBiCwWkbOraHeJiHwgIutFREXk1YO89ygR+cl9320i8qSI2CJUY5qwjxZu8j0+87DOHkZy6ERkn2IXnyza4mE0ded1alvV4opqvy2LSAzwLpCEUxzjOOA24Hzg/+ozQBMYcgtLuOK1uWzd4+yRNKBjPM/+/jDCwyy5ClXXj03hpAFO6dbcolKuen2elW839aouxZZck3HWE98DnApsBb4WkaGV2j0A3Af8GzgZ+Bl4X0ROqdTuIqAn8C37T4H3j3uw2ybDfd+7gcuAV2sQszEmBG3MymNuujNukdwmlmFdW3kc0aE7fZ8EazOqwbsG28sEaxfOKFZlCVQ9suXvCmAMcIqqvqmqs1T1CZwqgteKyJBDDUZVh5ffDrWvaVilZcqN7yxk6Wbn+0b7+BgmX3I4zd2N6UxoCgsTnjhvCL3btQAgfWceN75TMT3UmHpQ62JL7ufMBcBNqvqiqk4HzgM2APf7tUsCbgUeUdUn3KJM1wAzgEcqvewEVR2qqlfizMw4kH8Am4BzVXW6qr6EM0X+PBEZVuOf3hgTMvzXLZ1xWKegnN3T1S8xXLcjl9827/E4otrzMsFahrMOq7L+wPJq+g4Cdqnq2krnf3Xv+9UxNhNAnp62imnuos3mUeG8fOnhtG8Z43FUpjG0iI7ghT+MID7GSaZnpmby5LepHkdlQkhdii1NAopxZlOU9y0B3gEmiEi0e3oCTmGmNyv1fxMYJCLd/fpXuy+BiEQCJwHvqar/kO57QFEN4jbGhBhV3SfBOivIpgf68y928fHC4J0m6GWC9SlwlIj0KD8hIsk4Jdg/rabvNiBBRFIqnT/SvQ/+8iMGcCoG/r/vnO8+YQL/vnAY/TvGexyVaUzJbZvz7O8P8xW9+L8Za0OihKsJCHUptjQASFPVvCr6RgEpfu0KgTVVtKMG71NZTyCGSnG7a5PX1uL1jDFBbuHG3aS5RSFGdEuga5vg3a1o4qAOvuUfny3ZErSzVrxMsF4E0oFPROR0EZkEfAJsBJ4vbyQi3USkRETu8ev7Ks70iS/cRcFjReQ24AlgPs7VRxPktuzO56Z3F/mObz6hd1CVHDX1Z0yfJG6b0Md3fOv7i1m57YBLVIypqVoXW6qmb/nz5fe7df/FBJXb1VR5+wO996G+HmCFnowJZh8tCL69rw6kTYtoRvdqC0BmdiE/rd3hcUS141mC5ZZSHwesAt4A/gekAeNUNcevqQDh+MWqqunAUcAi4EHgC5y59C8AJ9RkmoUJbMWlZdzw1gLfbuSjeyfyxzGVByxNU3LdcT2ZOKgDAPnFpVz9+nx25xV5HJUJAbUqtuS2qUnfmrarqfJ+9fmaxpggVVRSxmdLnKl0UeFhnDqoo8cR1V0oTBP0tIqgqm5Q1bNVNV5V41T1DDd58m+TrqqiqvdVOr9cVc9T1S6q2kxVe6vqrapaXYEMEwQe/XIlCzbsBpyiFk+fP5QwqxjYpIkIj587mL7t4wDYkJXHn962ohemTupSbOlAo0UJfs+X3yfI/ivOK7erqYONfCXU4vUAK/RkTLCamZrBbvdi9Li+SbSMjfQ4oro7oX87YqPCAfh62Tbyi0o9jujQeV2m3Zj9fLV0Gy/9kAZARJjwfxceRuvmUR5HZQJBbJRT9KJlM+cDZPbqHTz29UqPozJBrC7FlpYB3d1S75X7FlGx5moZEI2zdqpyO2rwPpWtxVnTtU/c7vYlPWrxesaYIOZf3CLYpweWi42KYIK7TUtOYQnTVmz3OKJDZwmWCSgbduZx25TFvuO/ndyX4d1qtaTAhKiubWL59wWHUT6g+fz36/h0cXBOITCeq0uxpU+BSOBcv74ROPsxfqOqhe7pr3ASrgsr9b8IWOpWLawxVS1yX/M89/3KnYOTyFUXtzEmROzJK2a6W2W5VWxkSK1TP31oxVTHTxYFX+06S7BMwCgoLuWPb80nu6AEcIaIrxjVvZpepik6tlcifzu5r+/49ilLWJuZc5AexlSp1sWWVHURTon2p0XkShE5HqdEe3fgXr92GcBTwB0icrOIjBGR/+CsQb7TPxgR6S8i54jIOUAzoFv5sYgk+jW9D+gCvCcix4vIFcCzwBRVtSIVxjQRU3/bSlGpU3bg1MEdiIoIna/1o1La0raFM3tpZmomu3KDa8116PyXMEHvwanLfZsJd2ndjCfOGRKUG+WZxnHVsT04bYhzhSu/uJQb31lIUYnVtzE1V5diS67LgFdwii1NxUl6TlLVBZXa3eW2uRH4GmeE7DxV/axSu/OA991ba2CM37FvSqCb3E0AOrjv+xDwOnDJofz8xpjg9uGCTb7HZwbx3ldViQgP49TBzmd8SZky9bfg2p7FEiwTED5ZtJk3f94AOFVwnrtgeEgs1DQNR0R4+KxBdG3tLIFZunkv//rGNiE2h6aOxZbyVfVmVW2vqjGqeqSqzqziPUpV9UFV7aaq0ao6WFWnVNHuPvd9qrrNrNR2lqoe7b5vO1X9SxV7chljQtTGrDzmrXdq8SS3iWVY11YeR1T/gnmaoCVYxnNrMnK448PffMd/P60/gzq39DAiEyxaREfwzO+G+jYlfH7WOn5YHZx7ZhhjjDE19e3yisIPk4Z2CskZP0O7tKKbu2ny3PRdbMwKnmtIlmAZT+UXlXL9/xaQ55bgPG1IRy46sqvHUZlgcljXBG4+obfv+Ob3FpEVZHO1myIRiRaR40TkjyJyr4jc4z4+TkSivY7PGGMCmX9lvRP7t/MwkoYjIpw+tKIy4hdBNE3QEizjqXs+WUrq9mwAeiQ25+GzBoXkVRjTsK49ridHdneqTWZkF3L7B0tQtf2xApGInCgiU4DdwHfAv3GKQtznPv4O2CMiU0TkRM8CNcaYALUnr5hf0pwt7zq0jGFAx3iPI2o4pw3u4HtsCZYxNfDlb1t5f76zQDMmMoznLhxGi+iIanoZs7/wMOGp84cSH+P8/ny7fDv/+2WDx1EZf+7I1C84JcaHApOBS4FRQD+cIg6j3HOT3TZfichcETnOi5iNMSYQzVyVQWmZcxFxfL92IX1hule7OHoltQBg8aY9QTNN0BIs44nM7ELu/Khi3dV9pw2gb/vQvQJjGl7HVs145OzBvuMHpy5ntTs6agLCdJzNd0eqaoqq3qCqb6jqT6qaqqor3MdvqOr1qpoCjMSp8DfN08iNMSaATHP3vgIYH6LTA/2dMqhiFOvLpcEximUJlml0qsodHy5hV14xAMcj2mWvAAAgAElEQVT3TeL8w7t4HJUJBacM6sB5I5xStQXFZfz5nUUUlpR6HJVxDVDVC1X155p2UNWfVfVC/EqUG2NMU1ZUUsbMVCfBah4VzlE9WnscUcOb6DdNcOpv2zyMpOYswTKN7v35m3xXXxJiI3n4bFt3ZerPvacNoHvb5gCs2LqXx76y0u2BQFVr/R9CVVfVZyzGGBOs5qZnkV1QAsBxfRKJjgj3OKKG1yupBT0Tnc/1xRt3s2lX4E8TtATLNKpNu/K4/7PlvuMHzxhEUlyMhxGZUNPcLd0e4ZZun/xDGt+vyvQ4KlOZiKwTkUkHef5UEVnXmDEZY0yg8y/PPr5f6E8PBKea4ES/aYJfLQ38USxLsEyjKStTbnt/CTmFzpWX04d23GfY15j6MrhzK26d0Md3fMt7i9mRU+hhRKYKyUCLgzzfHOjWOKEYY0zgU1VfefYwgbF9kjyOqPGcss80wcBfh2UJlmk0r/6Uzpx1OwFoFx/N/ZMGehyRCWVXH9uDkT3bALAjp5Dbp1jp9iDTBcjxOghjjAkUq7bnsGlXPgAjurUmoXmUxxE1nj7t4ujhThNcuGE3W3bnexzRwVmCZRrFmowcHv1qpe/40bMH0zI20sOITKgLCxOePG8ordzfs+krM3jz5/UeR9W0icjpIvKyiLzsnrq6/LjS7SOcvbF+9TBcY4wJKP6bC4/v33RGr2D/aYKBvieWJVimwZWUlnHL+4spLCkD4IIjuzKmCQ1rG++0bxnDo36l2x/+cmXQ7KERoobi7HN1KaDAaL9j/9vxwM/A9Y0cnzHGBKymuP7K3ymWYBlT4T8z17J4424AuraO5a5T+nkckWlKJgxoz7nDndLteUWl3PHhbzZV0COq+g9VDVPVMECAi8qPK93iVfUEqx5ojDGOjOwCFrnfpXokNqdH4sGWsIamvu3j6OFWCV4Q4NMELcEyDWrp5j08M301ACLwr/OG0Dw6wuOoTFNz98T+JMZFA/DDmh28P2+TxxEZoDvwsddBGGNMMPjOb3PhE5rg6BU40wRPHtTed/xlAFcTtATLNJiC4lJufm8RJWXOaMHVx/bg8OTQ3xDPBJ6WsZE8eEZFUZUHpi5n+94CDyMyqrpeVW2+pjHG1MC+66+aZoIFwTNN0BIs02Ce+nYVq7Y7RcB6t2vBTSf09jgi05RNGNDety1AdkEJd3+81KYKNiIR+UBEBtWi3xAR+bAhYjLGmGCQX1TK7NU7AEiIjWRY1wSPI/JO/w7xJLeJBWD++l1s2xOYF0stwTINYm56Fi/MdvYIjXCrucVEhv5u4yaw/WPSABLcqoLfLt/O50sC9+pXCIoFForIDBG5XEQ6HqihiHQVkatF5HtgAdB0ahEbY0wlP6zZ4SsUNq5vO8LDxOOIvCMi+4xifbk0MD/HLcEy9a6guNTdc8g5vvH4Xgzs1NLboIwB2raI5t7TBviO7/t0GVm5RR5G1HSo6snABPfwJWCjiGwRkdki8qmIfCYiP4jINiAN+A9QDIxX1VM9CtsYYzw3za964AlNrDx7VYJhmqAlWKbePTdzLet25AIwqFNLrhvT0+OIjKlw+tCOjOvrfEDtzC3iH58t8ziipkNVp6vqWKAvcA+wGGdD4eOBsUAnYD5wJ9BHVcer6gyv4jXGGK+VlSnTVzoFLqLCwzi2V6LHEXlvQMd4urnTBOet3xWQa6otwTL1ak1GNv+ZuQaA8DDh4bMGERFuv2YmcIgI/zxzIHFuNctPFm1hut/iYdPwVHWVqv5TVU9W1WRVba6qLVS1u6pOVNVHVXWN13EaY4zXFm/azY6cQgBGprSxSszsO01QFb4MwFEs++Zr6k1ZmXLnh0spLnXmBl5+TLJNDTQBqUPLZtzhtx/bXR8tZW9BsYcRGWOMMfvzrx54fBMtz16VUwb6TxMMvHLtniZYItJFRKaIyB4R2SsiH4pI10Po309E3heRHSKSLyKpInJjQ8ZsDuzdeRv5NT0LgE6tmlnVQBPQfn9EF47u0QaAbXsLePiLFR5HZIwxxuxr2vKK/a/G97P1V+UGdoqnS+tmAMxdn0VGgE0T9CzBEpFY4DucufiXAH8AegEzRKR5DfqPAH4BooErgVOAfwFWqs4DGdn7fkF98IyBxEbZMLYJXCLCI2cPIibS+TP49q8b+WnNDo+jalpE5EIR+UlEMkSktIpbidcxGmOMVzbszCN1ezbgJBQdWjbzOKLAUXma4FfLAmsUy8sRrKuAHsAZqvqxqn4CTAK6AdccrKOIhAGvAdNVdZLbf4aqvqCqTzZ45GY/D3y+gr0FznehiYM7MLavXWUxga9bm+bcNqGv7/j2D5eQV2Tf6RuDiNwJvA70BOa4jyvf3miEOGo9k0JEYkTkcRHZ6s6imCMio6toFyYid4hIuogUiMhiETn7AK95lYisFJFCd1bGtVW0eVVEtIrb04f+L2CMCVT7bC5s0wP3M9GvmuDUANt2xcshhknAz/4LmVU1TUR+BE4HDpYojQH6A/t98JjGNzM1g88WbwEgLiaCe0/r73FExtTcpSOTmbpkCws27GZjVj5PfL2Ke+x3uDFcB/wInKiqnszt8JtJUYgzk0KBB3FmUgxW1dxqXmIyMBG4DVgHXA98LSJHq+oiv3YPALcCd+FUSfwd8L6InKqqX/jFcxXwPPAwMA2nuuJzIiKq+p9K752J8znqL7C+YRhj6sQSrIMb1KklnROasWlXPr+mZ5GRXUBSXIzXYQHejmANAJZWcX4ZTvJ0MKPc+xgR+VlEit0pJs+KSK3GT0VkfvmtNv2bqryiEu7+uOI/499O7hswv9zG1ER4mPDYOYOJcqtdvvJTGgs37PI4qiahLfCWV8mVqy4zKYYAFwA3qeqLqjodOA/YANzv1y4JJ7l6RFWfcGdbXAPMAB7xaxcB/BN4Q1XvctvdDbwKPCAikZVCKFLVnyvd1tflH8MYEzj25BXzS5qzrr1DyxgGdIz3OKLAIyK+USxV+Hpp4EwT9DLBag1U9S0mC0iopm9H9/5d4BvgBOAxnLVYb9VXgKZ6z0xbzaZd+QCM6JbA7w+vcY0SYwJGSlIcfz4+BXD+SP/9k6WUlqnHUYW8pYDXl2SrnEmBM7J2eg36FuN8DpX3LQHeASaISLR7egIQBbxZqf+bwCAR6e4eHw0kVtHuDaANFRcWjTFNwMxVGb7PofH92iEiHkcUmE72nyYYQOXavS7TXtU3mJr8BpXH/aaq3qOqM1X1CeAfwBkicsjze1R1ePntUPs2Vcu27OGlH9IAiAwXHjprEGFh9gfABKerR/ckJakFAEs37+WtX2wwoIH9HbhWRHp4GENdZlIMANJUNa+KvlFAil+7QqDyvl7lO1z392tHFfFUblcuya2gWyIiq0TkdhGxIk/GhIjpK/yqB/b3+lpU4BrSuSWdWjmT135NyyIzu9DjiBxeJli7cEaxKkug6pEtfzvd+28rnf/GvR9ah7hMDZSWKXd8+Jvv6sq1x/Wkd7s4j6MypvaiIsK4f9IA3/HjX6f6Nnc0DWIcsAlY6haZ+JeIPFbp9mgDx1CXmRQH61v+fPn9blWtfEGxqnZU8ZqV2wEsAm7BmZI4CfgeZ93W89XEfEA2Td6YwFFcWsaMVCfBah4VzlE9qvq6bKC8mmB7AMoCqJqgl0UullFxxc5ff2B5DfrC/iNg5cMnZXWIy9TA63PSWbJpDwDd2zbn+rEpB+9gTBAYmdKW04Z05LPFW9hbUMIjX67kiXOHeB1WqLrV7/FZB2ijwO0NHEdtZ1JIDfseSrsDxbMPVa1cLfALEckB/iIij6rq6upewxgTuOamZZHtVmY+rk8i0RE2OH0wpwzqwIuznRlVXyzZyh+O6uZxRN6OYH0KHOU/PUREkoFj3OcO5kucKRcnVTo/wb2fVz8hmqps2Z3PE1+n+o7/ecZAYiLtf34TGu6e2I/mUc7v85T5m5iXnlVND1NL3Wtwa+jpg3WZSZF1kL7lz5ffJ8j+CyiqakcVr9m60vMH8rZ7P6KadlWyafLGBI5vrXrgIRnapZVvmuCcdTtZ5e4d5iUvE6wXgXTgExE5XUQmAZ8AG/Gb5iAi3dw55veUn1PVnTjTIa4VkYdEZLyI/A24B3jNf8GyqX/3frqM3KJSAM4e1pmRKW09jsiY+tMuPoabTujtO77746WUlNqgeH1T1fU1uTVwGHWdSdHdLfVeuW8RFWuulgHROPt9VW6H3/uUz8yoHE/ldgdS4xEwY0zgUlVfefYwgbF9bF/R6ogIFx5VUWTtvzPXehiNw7MEy91fZBywCqdK0v+ANGCcqub4NRUgnP1jvR/4K84c9C9w9lR5HKfsrmkg3y7fzrfLnf/xE2IjuWtiP48jMqb+XTIymT7umsKV27J542creBGi6jKT4lMgEjjXr28EcD7wjaqWL+D7CifhurBS/4uApW7VQnA2W95xgHZZOJUND+YCnORqbjXtjDEBbG1mDhuznOrMw7slkNA8yuOIgsNFR3UjLtpZ+fTJ4i1szKpcf6hxebkGC1XdAFS5m71fm3SqmA/vLhh+koNvSGzqUUFxKQ98XnER9a6J/Wlt/+ObEBQZHsYDZwzkvOfnAPDkN6uYOKgDSfG2x1tticjLOAnA1apa6h5XR1X1igYM60XgBpyZFHe78T1AFTMpgLXA/ap6vxvYIhF5F3ja3aMqDedCX3f8kiRVzRCRp4A7RCQbWICThI3DrxS8qhaLyN9xNhbejLPR8DjgcuBPqlrkF8sbOOXg1+CMjp0JXAo8r6reX7o1xtTadysrqgeO7WujVzUVHxPJH47uxnMz11Japrw4ex33nz7Qs3hqlWC5UyIScT6MdlRRptaEoJdmr2ODe0VgeLcEzh7WyeOIjGk4R3RvzVmHdeLDhZvJLizhoS9W8PTvDvM6rGB2Kc5nxnVAqXtcHQUaLMFS1VwRGQc8hZO0CDAd+EsNZ1JchrM58INAK2AxcJKqLqjU7i4gB7gRaA+kAuep6meV4vmviChOhcDbcDYtvkFVn/Nrlo0zonU7zj5iCqwA/gz4tzPGBCH/BGucJViH5PJR3Zn8QxqFJWW8O3cjfz6+F21bRFffsQHUKMFyF+dOBM4BjgO6Vnp+A06Z2CnA1CrK0Zogt2V3Pv83w7kwKgL/mDTANr0zIe+OU/rx7fLtZBeW8PGiLfzuiK4c1aON12EFJVUNO9ixV+o4kyIfuNm9Hax/KU4S9mAN4nmeg5RbV9Us4IzqXscYE3z2FhQzL92pr9OxZYxvqrqpmbYtojn/8C68Pmc9hSVlvPJjGrdN6OtJLAf9gBORcBG5HliPM9/8TGAdMBl4DHjCfbzOfe5TYIOIXG8bHoaWh75YQX6xU9jid4d3ZWCnlh5HZEzDS4yL5pYTKwpe3PPJUoqt4IUxxpgGMHvVDkrc/UXH9k2yC9m1cNWxPQgPc/7dXp+znuyCYk/iqO4K4gqcan1f4IxctVLV41X1alW9Q1Vvdx8fjzM9YgwwFXiI6isemSDx87qdfL5kKwDxMRHcNqGPxxEZ03guOqob/TvEA7Bqew6v/pjubUAhRETCKh23cC/Q3SMiVkHHGNOklG8uDFY9sLa6tI5l0pCOAGQXlPDmzxs8iaO6BOs9IFlVr1XV2Qeb+qeOWap6Lc4i3/fqM1DjjZLSMu77dJnv+JYT+1hhC9OkRLgFL8o9PW0V2/YUeBhRaBCRF6goTV5ege8H4FngPmC+iAz1JjpjjGlcZWXKTDfBiooIY2SKTUevrevGVOyKMfmHNArcGViN6aAJlqre7c73PiSqmqWqf699WCZQvPXrBlZuczZs69s+jguP7FpND2NCz/BuCZw3ojMAuUWlPDjVBujrwWjgY7/js4DBOFX9RgLbgTs8iMsYYxrdb5v3sCOnCICje7QhNsrTQt9BrXe7ON8GzTtyCpkyf1Ojx3BIi4zdaRsHrHkoIgP8NwQ2wS0rt4h/fbPKd3zfpAFEhAfEunRjGt3tJ/WlZbNIAD5fspUf1+zwOKKg1xGntHm5k4HfVPU/qvozTqGHkZ5EZowxjcyqB9avP46tGMV6ftZaShp5/fShflu+D+cK44EMBO6tdTQmoDzxTSp78p3FgacO7mDV00yT1qZF9D7rD63gRZ0p+34GjcUpkV4uA2c7EGOMCXn+668swaq7YV0TOLJ7awA2ZuUz9betjfr+9T0cEQuU1PNrGg8s3byHt391FgY2iwznzlNsvbkxvz+iK4M7OxU012bm8r+f13scUVBbA0wAEJEjgS7sm2B1BnZ5EJcxxjSqjOwClmzaA0BKUgu6tI71OKLQ8MexKb7H/5m5lsbcRaraBEtEuorIaBEZ7Z7qW35c6XY6cA1OyXYTxFSVez9dRvnv4fVje9KxVTNvgzImAISHCfee1t93/NS01ezOK/IwoqD2HHC6iCwFvgTSgW/9nj8W+M2DuIwxplHNTM30PbbRq/ozuldbBnR0qgCv3Ja9zyhhQ6vJCNZlwExgBs6Ujrvcx5VvHwEjgEcbIlDTeD5ZtIX5650Lx11bx3LlsT08jsiYwDG8W2tOHdwBgD35xTwzfbXHEQUnVZ0MXA6swil2cZKqFgGISBugNfCudxEaY0zjmLHSyrM3BBHhj2MqRrGem7G20d67JiVKPsa5sijAy8ALwJxKbRTIAeapqjcF5029yCks4aEvVviO/35qf2Iibc9oY/z97eS+fLN8O0UlZbwxZz0XHdWNnoktvA4r6Kjqq8CrVZzfCQxv7HiMMaaxFZWUMXu1UzQpLiaCEckJHkcUWk4a2J7ubZuTtiOXeet38WtaFke4a7MaUrUjWKq6WFVfcz8I/wH82z32v72uqh9achX8/v3dGjKyCwEY3TuR8f3sSooxlXVOiOWqY7sDUFKmPDR1RTU9jDHGmP3NS88ip9ApXzC6VyKRVq25XoWHCdeMrpiJ9dzMNY3yvof0X1FV/6GqSxsqGOOtdZk5TP7BWUIX4a41ERGPozImMF03JoXEuGgApq/M4IfVVrbdGGPMofEvzz7W1l81iDOHdaJdvPN5PTM1k+Vb9jb4ex40wRKR02r7wiIyqbZ9jTce+Hw5xaVOZYvLR3W3KU/GHESL6AhuPbG37/iBz5c3+j4bxhhjgtt3buEFERjTx3amaAjREeFc5VdP4D/fN/xarOpGsN4VkXkicrGIVPttW0TiReQyEZkPvF0/IZrGMHt1JjPcKjaJcdH8aVxKNT2MMecM70L/Dk6FotTt2bw7b6PHERljjAkW63fmsi4zF4DBnVvRtkW0xxGFrt8f0ZVWsZEATF2yhfQduQ36ftUlWH2BlcArwHYR+UZE/ikiV4jIWSJytohcKSKPiMh3wDbgRWCZ29cEgdIy5Z9+a0huO7EPcTGRHkZkTHAIDxPuPrVij7gnv1nF3oJiDyMyxhgTLPynB46z6oENqnl0BJccnQxAmcLzsxp2V6mDJliqukFVLwJSgGeAZOAOnCTqfeA9nKqCfwU6AP8Ceqrqxapql3KDxAcLNrFyWzYAfdvHcfbwzh5HZEzwGNmzLSf2bwfAztwi/m9G4yygNcYYE9z2SbBs/VWDu3RkMs3cyti784oadOPhmpRpR1XTgDuBO0WkHdAPSMQpz54JLFfVzIO8hAlQeUUlPPF1qu/4ron9CA+zwhbGHIo7T+nHjNQMikuVV35I58IjutG1TazXYQUVEUkAPgBuUdWFXsdjjDENKbewhF/WZQHO0ozyDXFNw0loHsXDZw2iT/s4+nVo2H/vQ64FqarbVXWmqr6vqlOA2Th7ZJkg9OKsNF9Z9jF9Ejm2ly2wNOZQJbdtzqUjkwEoKi3j4S+tbHstRAFjANsExhgT8n5cs4MitzDS2D6JhNnF7UZxxmGdGjy5ghokWCKS7K63alXpfKyIvATkAltFZLuIXNFQgZr6l7G3gOdnOZVUwgTuOLlfNT2MMQdyw7hetG4eBcCXS7fxy7qdHkdkjDEmUM1ItemBoawmI1g3Ay8BeZXOPw1cDhQAC4EWwAsiMr5eIzQN5slvV5FXVArA+Yd3oU/7OI8jMiZ4tWwWyU3je/mOH5i6nLKyhpvfbYwxJjipKjNWOitrIsOFUTZ7KOTUJMEaBXyiqkXlJ0QkESe5WoNT1GIEMAjYAdzQEIGa+rVy217ec0tKx0aFc9MJvavpYYypzu+P6EqvJGdHi6Wb9/LBgk0eRxRUSoH1QL7XgRhjTENavnUv2/YWAHBE99a0iK5RSQQTRGqSYHXBKbvu72S371OqmgWgquuA14Ej6jVC0yAe+mIl5RfXrz2uJ0lxMd4GZEwIiAgP4+5T+/uOH/s6ldzCEg8jCh6qukNVu6vqHK9jMaEju6CYldv2Mi89iw078ygoLvU6JGOY4Vc9cKyVZw9JNUmZWwC7Kp07CqeC4PRK51OBNvUQl2lA36/KZNYqZ2i6XXz0PrtbG2Pq5rjeiYzpk8jM1Ewyswt5/vu13HxiH6/DMiYk7cgpZGNWHpt357N5Vz5bduezeXc+m9zHewv2v8DRunkU7eJj6NAyhvYtY2gf79x3aBlDr6Q42re0C46mYVl59tBXkwRrI05Zdn+jgd2quqqK18uu6ZuLSBfgKeAEnEqE04C/qOqGmr6G+zp3AA8BP6rqqEPp29SUlikPf1FR4ezWE/vQLCrcw4iMCT13T+zH7NU7KC1TXpydxkVHd7NR4gBVl88hEYkBHgAuAloBi4DbVXVWpXZhwO3ANUB7nIuR96vqB1W85lXALUB3IB1npsh/q2h3BnAvzufzdpz9KR9W1ZAeoskrckpbz1qdyezVO1iTkXPIr5GVW0RWbhErtu6t8vmUpBaMSmnL6N5tObJ7G5rb9C1Tj7Jyi1i4cTcA3drE0r1tc48jMg2hJn81fgIuE5FXVHWZiEwC+gPvVNF2ILC5Jm8sIrHAd0AhcAnOiNiDwAwRGayquTV8nR7AXUBGdW0NTJm/0bepcL8O8Zw1zDYVNqa+pSTFcd6ILrz96wbyi0t5dvpqHjxjkNdhmUrq4XNoMjARuA1YB1wPfC0iR6vqIr92DwC34nxWzQd+B7wvIqeq6hd+8VwFPA88jJPoHQ88JyKiqv/xazcBZ8+wyTiFqA7DucgYh5PIhYyyMmXFtr3MWrWD2aszmZe+y1fa+mDCBNrFx9CxVTM6tWpGfLMIMvYWsn1vAVv3FJCZU8iB9hhdk5HDmowcXv0pnchwYVjXBEb3TmRUSlsGdmppe0WaOvl+VYbvd29snyRE7PcpFNUkwXoAOAdYIiI7caYAFgNP+Ddyr9CdDnxWw/e+CugB9FHVNe5rLAFW41zle7KGr/Mf4H9AH2q4cXJTlVtYwr++qRh0vNs2FTamwdw0vhcfL9xMfnEpb/+6kcuP6U6PxBZeh2X2VevPIREZAlwAXK6qr7jnvsdZs3w/MMk9l4STXD2iquWfmzNEJAV4BPjCbRcB/BN4Q1Xv8mvXEXhARF5S1WL3/CPAD6p6tV+7FsDdIvKUqm6r07+KR1SVrNwi1mbmsiYjh7npWcxencmOnKIq24vAwI4tGdAxnk6tmjnJVIKTULVvGUNk+IGXmReXlpGRXci2PQVs21PA1j35bNldwLz1Wfy2eY/vC3BxqfJLWha/pGXx+NeptIqN5JiebRnTJ5FxfZNo0yK6If4pTAj7zq0eCDY9MJRVm5Co6loRGYMzFSEFmIczDWFBpaZjgd3ARzV870nAz+Ufau57pYnIjziJWrUJlohcAAwDfg98WMP3bbJemLXOt6nw2D6JHJPS1uOIjAldSfExXDGqO/+esYbSMuWJb1J57sLhXodl9lWXz6FJOBcb3/XrWyIi7wB/E5FoVS0EJuBsovxmpf5vAi+LSHdVTQOOBhKraPcGcBlORd8Z7pTGocDVVbT7B04Rqleq/ck9VFJaxsZd+azNyGFtZvktl7WZOezOKz5o33bx0Yzulcix7ohS+d5zhyoyPIxO7uhWZVm5Rfy0dgez3VGzLXsKfM/tzitm6m9bmfrbVkRgWNcExvdrx/h+SaQktbDRCHNQJaVlvjXwsVHhHNmjtccRmYZSoxEfVZ0HnFZNm+k4pdpragDwSRXnlwHnVtdZRBJw5s3/VVWz7I/awW3fW8ALs9YB7qbCp9imwsY0tKuP68H/flnPrrxivvhtGws37OKwrgleh2Uq1OVzaACQpqqV94hchpNQpbiPB+BMQVxTRTtwptynue0Alh6k3YwDtXMTwzy33SETkfnlj4cPP/QLAX//eClT5tdsW4Ki0jJKa7hHXHREGEf2aMPoXm0Z3TuRXo2QxLRuHsWpgzty6uCOqCrrduQye1UmP6zZwZy1O8l1949UhfnrdzF//S4e/Wol3drEcnzfdozvn8Thya0POoLWGEpKy9iQledLXte4Ce32PQWMSG7N7Sf3rTLBNA1n4cbd7Ml3LiIck9KW6AhbAx+qvJxS15r9qxMCZAE1+QbyOLAKeLU+gqnrh0uge/KbVeS75Wl/d0RXerezTYWNaWjxMZH8aVwv7v98OQCPfLmSd64+yq5y+3HXQSXirH/aUUXC0pDq8jl0sL7lz5ff71bdb8VPVe2o4jVr2q78nCeXxItLy3yfMbXVpnkUPRNb0DOpOT0TW9C3fTwjkhOIifTuS6iIODEltuDSY7pTVFLGvPVZTF+RwbQV21m/s+LXdf3OPF7+MY2Xf0wjPiaCY3slMqRLS3caY0taxkY2SIwFxaWszcxh9faKJGpNRg7pO3MpLq06kf108Ra+Xb6dv4zvxeWjunueDDYV05Zv9z226YGhzes1S1X9n1/tNw8RORa4GBhWxYeWqWTF1r28N9/ZVLh5VDg3jbdNhY1pLBce1ZWXf0xj0658fknLYmZqJmOb8AerONnlRJy1vccBXSs9vwH4HpgCTG2Ev/G1+hxy29Sk76G0O1A8NW1X68xdVX1XFkeMGHHI/+aJcea64IkAACAASURBVNH0SKxZNbSIMKFr6+a+RMq5NadVbO2m+zWmqIgwRvZsy8iebbl7Yj/WZuYwbUUG05ZvZ8GGXb79JfcWlPimEpbrnNCMgR1bMrBTPAM6tmRAp/hDqi5aVFLGuh05rNqew+rt2azans3q7U4iVcMBQQAiw4XiUiW/uJSHv1zJhws28+CZAzk82aarNSRV5etlzvJIETi+X9P9HGgKvEywDnSlLYGqr8z5ex6netImEWnlnosAwt3jfHfue43V9cMlkD361Urfgt3rxvQkMc4W5RrTWKIjwrn1xD785V2nqNyjX61kdO/EJldgRkTCgWtxqtx1xtnSYx7wLbATZ/P6BKAncCbORbTNIvII8N8GKj9el8+hLColh359y58vv09wKwFqNe1w49nq1671QdpV1srv+UZ1y4l9uKWJ7fcmIqQkxZGSFMe1x/UkK7eIGSudka1ZqzJ9UwnLbdrl7M/11bKKGiRJcdH7Fcrw/8tQPtidX1zK+p15NZ5aGR4mdGsdS88kJ4FNSXKS2J5JLSgtVR79aiXvzHUuvKZuz+bc/87h3OGdueOUfrVe12YObtX2HNLdEc9hXRNs644Q52WCVT43vbL+wPJq+vZzb9dW8dwu4Cbg6TpFFyJ+XreTmakVmwpfMco2FTamsU0a0pEXZq1j+da9rNyWzccLN3P28Ca3RcIKnD2g3sKp/PrDgUan3FGuY3Gq9D0E/BmnUmx9q8vn0DLgTBGJrTStsT9QRMWaq2VANE7iuKZSO/zep3yt1QD2TbAO1m5OeSMRSQZiaxC3aSCtm0dx9vDOnD28M4UlpaRuy2bp5r0s3bKHZZv3sGJbNkUl+5aYz8gu9BWfqo3IcKF72+b0bhdH73Zx9EpykqlubZoTFXHgaX+PnD2Yc0d05v+3d99xUpZX/8c/Zwu79CIdlo40QRQ0KKgI9t6C5mcLiS1GY83z2JJHjUnMEyOaGEs0j0nsPaAmKghoLIigqHSW3nuvy+75/XHPDsOwyy7s7NwzO9/36zUvmHuva+awwF5z7nOVu9+aGj265bXJSxg9YyV3nNadYf0LyMqwm0DV7f2YxPrUXi1CjESSIcwEaxTwkJl1cvd5EB0gBgJ3VND3xDKuPQJkAzey72LijOQe3KUqddPQQ3WosEgIsrKMO07vzhX/NxGAh0fP5sw+rUJdWxKCV4GH3b3CCksk8foY+NjM7iK4aVYdqjIOjSLYte/7wN8jfXOAi4EPYmZRvEeQcF0aaV/qMmBqZAdBCJKlNZF2Y+LarQM+BXD3RWb2TaTdM3HtioB/V+LPLdUsLyebPm0b0adto+i1ouIS5q7eEiRdSzcyfdkmpi/fxLZdu6NtYu84xN5+yMky2h9Sh24t69O1ef1IQlWPDk3rHvT6qX7tm/DOjYP422cLGDF6Nlt3FbNhWxF3vPkdr05azK/P702PVg0O6rVlX+9NjU2wWoYYiSRDmAnW08ANwEgzu4fg58qvgMUEUwABMLP2wFyCU+/vB3D38fEvZmYbgJyyvpapRk9fydeLgtPCOzWty7D+GXfHXCRlHNe1KQO7HMKnhWtZumE7z32+kKuPz5yKsrvfc5D91gG/SHA4paoyDk0xs1eAR8wsl2AnwJ8AHQmSn9L4V5nZCOBOM9sMfEWQhA0h2Aq+tF2Rmf2C4GDhpQRJ1hDgR8CN7h57GNRdwDtm9hTwEsFBw/cAj6brGViZIDc7i+4tG9C9ZQMuSpEKdk52Flcd14kz+7TiV+9M51/fBf98vlq0gbP+9AkjLu7LOYe3DjnK9Ld43TamL98EQPeW9Wl/SOXWK0r6Cm3bGHffSjB4zCY4v+MFggFqiLtviWlqBJUpbXFzAIpLnN+/Pyv6/LZTupGjXYJEQmNm3HHanuMRHhtXGN2uNxOZ2S/N7LD9fL2Xmf2yOmNIwDg0nODMqQeAd4EC4LQyzom8O9LmJuB9ggrZMHd/Oy6eJwmStGGRdj8AbnD3P8e1+xfBJiEDIu1uIZhKWVHVTaRMrRrW5vFL+/Hs8KNo16QOEHyO+MU/p7Jua9kHPUvl7T09UNWrTGDahG9f/fv390mTJoUdRpW8NmkxP3/9WwB6t2nIqBsGamtokRRw40tf8/Y3ywC47oTO3HF695AjOnBmNtnd+1fxNUqAy9z9xXK+fjHwortn1DzKVFATxkA5eDuKirnhxa8ZMyPYUvzS77Xj1+cfyDGnEu/7T37GlwuCfXP+fdNxmnqZxio7/qmkUQPtKCpmxOjZ0ef/fVp3JVciKeL2Uw4lNzv4//jsp/NZvnF7yBGlrDrA7gpbiUhC5edmc/+5vagdWSP64sRFTF26MeSo0tfqzTuZtDBIrto1qUP3ljqHNBMowaqBnp+wkGUbdwAwqEtTBnVtGnJEIlKq/SF1ufR77QHYubuER0bPCTmi5DGzdmZ2vJkdH7nUvfR53ONc4FpgXojhimSs1o1q89MTOwPBZhv3jpqGZjwdnDEzVkY3LDm1Vwvd8M4QSrBqmM07ivjzuD2bKP7XaZl1LolIOrhhSBfqRnb0fG3yYuas3BxyREkzHBgPjCPYUOLuyO/jH28B/YHfhRKliHDVcZ2i67EmLVzPyCnLQo4oPWn9VWZSglXDPP3xPNZvCxbOn9m71V5bxIpIamhaL49rjg/uDpc4/O69WRX0qDH+SZBk/Zhg44inCXbJi30MJ9jAoZO7/y2cMEUkPzebX5zVM/r8N/+awZadmrV7IDbtKOLTwjUANKufx5HtGlfQQ2qKMLdplwRbvXknz3wSHKmSnWXcesqhIUckIuW56riOPDdhIWu27GTMjJVMWrCO/h2ahB1WtXL3b4BvILr1+RvuPjXcqESkPCf1aM4Jhzbjo9mrWbV5J4+NLUzLjXnCMm7mKoqKg/mBJ/dsocObM4gqWDXIY2PnsG1XMQDD+relc7N6IUckIuWpm5fDTUO7RJ///v1ZGbXGwd3vU3IlktrMjF+e3TO6Mc9fP5nH/DVbQ44qfXwwbWX095oemFmUYNUQi9Zu48WJiwDIy8nipqGqXomkuouPakfbxrUB+GL+Oj6JTCWpiczs7Cr0PSeRsYhI5XVuVo8fDewIQFGxc//b00KOKD3sKCpm3KxVANTPz+GYToeEHJEkkxKsGuLh0bOiZegfDuxAy4b5IUckIhWplZPFzSftuRnyUM2uYr1iZpPM7Aozq7C8bmYNzGy4mU0GXkpCfCJSjhuGdKFZ/TwAxs1azdiZKyvoIZ/MWROdVTS0e3Nq5egjdybR33YNMH3ZJkZGDi5tkJ/D9Sd0qaCHiKSK849oQ5fmQb7xzZKNjJ5eYz+4dAdmAs8CK83sAzP7tZn92MwuMLMLzewqM3vQzMYCKwg2wZgW6SsiIamfn8udMWuv7n97Ojt3F4cYUerT7oGZTQlWDfDQB7OiZyxcN7gzDevkhhuQiFRadpZx68l7qlh/+GA2xSU1r4rl7ovc/TKgC/Ao0AG4kyCJeg14FfgL8F9AK+APQGd3v8LdF4cStIhEnde3DUe2C3YmXrB2G3+NbKol+9pdXMKYGcHNsrycLE7o1izkiCTZlGCluYnz1zF2ZjDHt3n9PIYf2zHkiETkQJ3WqyW9WjcAYNbKzbzzbc09b8bd57v7Xe5+KEEiNQS4BLgYOBFo4e493P0X7r4wzFhFZI+sLOO+cw6j9Jzcx8YWsmLjjnCDSlETF6yLHplz/KHNqFNLm3ZnGiVYaczd+d17M6PPbzqpK7Ujh5eKSPrIyjJuP3XPoeAjRs+mqLgkxIiSw91Xuvt4d3/N3V9394/cfXXYcYlI2Xq3bcglRxUAsG1XMb/994yQI0pN2j1QlGClsbEzVzF54XoAOjaty7D+BSFHJCIHa/ChzejfPjiEcsHabbw+eUnIESWfmWWZWfOw4xCR8t1+Sjca5AcVmZFTljFx/rqQI0ot7h5df5WdZZzUQz/SMpESrDRVUuL84YPZ0ee3nnwoudn66xRJV2Z7V7H++OEcdhTVrEXkZtYhsqFFo7jrdc3sGWArsNzMVpjZj8OJUkT255B6eXutG/2fUdNq5LrRg/Xtko0sj0ydHNCpCY3q1Ao5IgmDPpGnqfemrWD68k0AdG9ZnzN7two5IhGpqgGdDuG4rk0BWL5xBy9+sSjkiBLuVuAZYFvc9RHAj4AdwNdAfeAvZnZScsMTkcq4bEB7urWoD8CM5ZsYOWVpyBGlDu0eKKAEKy0VlzgPj95TvbrtlG5kZVmIEYlIotx+yp4q1p/HFbJ15+4Qo0m4QcBId99VesHMmhEkV4UEuwb2B3oDa4AbQolSRPYrJzuLe87qEX3++Pi5lKiKBeydYJ3SUwlWplKClYZGTllK4aotABxe0Ejze0VqkMMLGnFKzxYArN26i799tiDcgBKrgOBcq1inE4xFI9x9HYC7zwP+ARyd3PBEpLIGdWnK4QXBbN/CVVv4oOae4Vdphas2M3f1ViD4Wd6yYX7IEUlYlGClmaLiEh4ZMyf6/PZTDsVM1SuRmuS2U7pFt0J+6qO5bIxs91sD1APWx10bADjwYdz1WcAhyQhKRA6cmXHDiV2izx8fX4h7Zlex3o/ZPfA0TQ/MaEqw0szrk5ewaF2wfOHojk0Y1KVpyBGJSKJ1a1mfcw9vDcCmHbv5y3/mhhxRwiwGesRdOx7Y4O6z467nAJuTEpWIHJSh3ZtH12J9u2QjnxSuCTmicO29/qpFiJFI2JRgpZEdRcX88cM91avbTlb1SqSmuvmkQ8mOrK189tMFrNmyM+SIEuIzYLiZ9QIws3OAnsD7ZbQ9DNDKeZEUlpVlXH9i5+jzx8YWhhhNuJZt2M63SzYC0LV5PTo1qxdyRBImJVhp5KWJi6Jbfx7XtSnf66TZMyI1VYeYs+227Srm8XE1oor1KyAP+NbMVgFvAUXAQ7GNzCwLOBf4NOkRisgBObN3K9o1qQPAF/PXMWlBZp6L9UFM9eq0wzQ9MNMpwUoT23bt5s8xH7BidxoTkZrpZ0O7UCsn+DH9/ISFLNuwPeSIqsbd5wKDgX8BawkqVye5+1dxTU8ENhAkYCKSwnKys7juhD1VrMfH14ibQQfsPW3PLjGUYKWJf3y+MDpF6OSeLaI794hIzdWqYW0u+157AHYVl/CnsXMq6JH63H2Su5/t7j3c/Qx3/08ZbT50997uPjqMGEXkwFzYrw0tGuQBMHbmKqYt2xhyRMm1avMOJs4PKndtGtWmV+sGIUckYVOClQY27SjiyY/23BGKPUFdRGq260/sTJ1a2QC8NmkJi9bGn9ErVWFmWWZ2p5ktMLMdZvaNmV14AP3PM7OvI30Xmtk9ZpZdRrtBZvaZmW03sxVm9rCZ1S6jXS8z+8DMtpjZWjN71syaxLUZbGZexmPDwX0XRKomLyebq4/rFH3+RIZVsd6YvJTSY8DO7NNK6+NFCVY6+L9P5rMhsk3zWX1a0aOV7oyIZIqm9fIYPrADALtLvEZUsVLMr4B7gccIzuSaALxmZmdU1NHMTgXeAL6M9H0UuAf4TVy7PsBoYBVwVqTNcOBvce1aA+OB2sBFwE+Bk4B3IuvS4v0MOCbmcVKFf1qRavKDo9vRuE4uAO9+t5x5q7eEHFFyuDuvfLko+rx07axkNiVYKW791l389T/zAcgyuEXVK5GMc/VxnaiXlwPAm18vZf6arSFHVDOYWXPgduBBd3/I3ce5+7XAOODBSrzEg8An7n5NpO/DBMnVLWYWuwjjPmAJ8P3I9MdngJuAYWZ2ZEy7nwO5wNnu/p67vwxcSpA8nVfG+89w9wkxj0kH9h0QSZy6eTkMH9gRAHf2mnlTk30+by0LIjMLju7QhC7NtXughJxgmVmBmb1uZhvNbJOZvWlm7SrRr7+Z/cXMZprZNjNbZGYvmFnHZMSdTH/5zzw279wNwAVHtqWztv0UyTiN6tTiR4OCH2/FJc6fPlQVK0FOBWoBz8ddfx7ovb8xxcwKgL5l9H2OIEk6PdIuFzgNeNXdY0+MfhXYRbBbYqlzgHfdPTrVz90/BhbFtRNJSVce02HPzaCvlrI0zTfmqYyXJy6O/v6So1W9kkBoCZaZ1QHGAt2BK4HLga7AODOrW0H3S4BewB8JBrE7gCOBSZFBr0ZYtXkHf/t0AQA5WcZNQ7uGG5CIhObHgzpSPz/44PLPKUspXJUZ02+qWS9gJxB/eM+0yK89K+gLMDX2orvPB7bF9O0M5JfRbgcwt7RdZD1Wx/h2MfGUFcsLZlYcWav1YmVuUJbHzCaXPg72NUQa1snlsgHBxjy7S5ynP54XckTVa/3WXbw3Ndg9sH5+Dqcf1irkiCRVhFnBuhroBJzn7v9095EEd+/aA9dW0Pd37j7Q3R9394/c/UWCO4SNI69bIzwxfi7bi4oBuPioAgoi50yISOZpWDs3uoi8xOFRVbESoQmwwd097vq6mK/vry/A+jK+tj7m6/trty7m640Bq0Q7gI3AH4CrgCEE68hOAj6PTHsUCc2PB3UkL3K8xMtfLqoph6SX6c2vl7KruASA849oQ+1a++xvIxkqzATrHGCCu0fvHEbu/H1KBVMh3H11GdcWAquBNgmOMxTLNmznhQnBoslaOVncOETVK5FMN3xgBxrWDhaRv/PtMmat2BxyRKnFzE4qZ3e9+Mf40i5AfHJVer3Ct4v8WlH/RLfD3b9299vd/e3ITcZHCG4ytiDY+OKAuXu/0sfB9Bcp1ax+HhcfFUwm2lFUwv99Mj/kiKpH/OYWlxx10AVkqYHCTLB6cWBTIfbLzHoAzYEZBxNMqk2PeGxcYfSuyOUD2tOyYX7IEYlI2Orn53LN8UEVyx0e/XB2yBGlnM+AHpV4XBFpvw5obPvuqdw45uvl2V+Vq1HM1/fXrnHM19cTJFcVtStT5LDm2cBR+2snkgzXHN+JnKzgv9Vzny9k4/aiCnqkn68WbWD2ymCq9uFtG9JTZ19JjDATrCaUPxWicRnXy2VmOcCTBBWsv1Y9tHAtXreNV78MFk3Wzs3mJ4M7V9BDRDLFlcd2oEndWgD867sVTF+2KeSIUoe7b3P3mZV4lN52ngbkEayTilV6k2/6ft6udJ1Wr9iLZtYBqBPTdy7BOq/4dvkE0+Snl8YOLIhvFxPP/mKJvixlV8BEkqpt4zqc2zeYULR5526en7Aw5IgS7+WJMdWro1W9kr2FvU37wU7NiPcYcCxwmbuXlbRVHEgKTY94bGwhuyMn1v1wYAea1ssLOSIRSRX18nK49vg9B3o+MkZVrCp4j2Anv0vjrl8GTI1MWy9TJEn7ppy+RcC/I+12Rd5nWORmYKmLCJK7UTHXRgFnmlnD0gtmNohgbXJsu32YWX/gUOCL/bUTSZafDO5MaW34r5/MZ/uu4nADSqDNO4p459vlANSplc3Zh7cOOSJJNWEmWLGLgGM1puzKVpnM7LfANcCP3P2DBMUWmoVrt/L6V0sAqFsrm2tiTkYXEQG4/Jj2NK0XVLE+mL6S75ZsDDmi9OTuq4ARwJ1mdquZDTazJwg2jrgrtq2ZfWhm8bsN3gWcYGZPRfreQnCI8KPuviKm3b1AAfCqmQ01sx8T7IL7urvHTkv/PVAMjDKz08zsYuAFYCLwVkwsL5jZA2Z2gZkNMbPbCJK4pcCfqvhtEUmILs3rcfphwXFw67bu4qWYik+6GzllWXQTsnMObx3dml6kVJgJ1jSqNhUCM7ubYIv2m9z9uQTGFpo/jS2kOFK9Gj6wI40jU4FERErVqZXDdSfsmdWmKlaV3A08QHDw7/vAQGCYu78d1y4b2OtTlLv/i6ASNSDS9xaCg4bviGs3heDMrVbAu5E2/yA4oiS23VLgRIKq2hsEU9/HAWe4e0lM06kEG0U9G3nfm4E3ge+5+5oD/QaIVJfrB3eJ/v6pj+eyo6hmVLFejtnconRDD5FYYSZYo4ABZhYt0UTmrg+kgqkQkbY/IxgU73b3GnHHbv6arbwZqV7Vz8vhquNq3LnJIpIglw1oT7P6wfThD2euYsriDRX0kLK4e7G7P+Du7d09z937uPvrZbQb7O4dyrj+prsfHunbzt3vd/d9PkW6+8fufoy757t7C3e/ObLuKr7dd+5+srvXdffG7v5Dd18b1+a3kTgbunuuuxe4+zXuvryK3w6RhDqsTUMGd2sGwMpNO2vEWqypSzcydWmw9rV7y/r0LWgUckSSisJMsJ4mWNA70szONbNzgJHAYuCp0kZm1t7MdpvZL2OuXQI8QjAlYqyZDYh5HPAOhKnijx/OIVK8YvigjjSqo+qViJQtPzebn8ZsgDNitKpYIpJ6bju5W/T3j4+fy5adu0OMpupe3mtr9gL23YRUJMQEy923Esxznw08RzDPfD4wxN23xDQ1gqkZsbGeFrl+GvB53OPxag++GhSu2sLIKUuB4DTwHw9S9UpE9u+So9vRskFwhMNHs1czeeF+d/IWEUm63m0bckbvPWux0vlcrG27djPy62UA5OVkcf4RbUOOSFJVqLsIuvsid7/Q3Ru4e313P8/dF8S1WeDu5u73xlz7YeRaWY/BSf5jJERs9erq4zpFDxMVESlPfm42Px2yZ43DiNFzQoxGRKRst558KJFjsXj643ms37or3IAO0rvfLmdzpAJ3Ru9WNKyjz2pStrC3aRdg9srNvP1tcEekYe1chg/sEG5AIpI2hvVvS5tGtQH4pHANX8xbW0EPEZHk6tK8frTas3nnbp78eG7IER2clyNnlEIwPVCkPEqwUsCjH87BI9Wra47vRP183RERkcrJy8nmxpgq1h9Gz8ZdZ82KSGq5+aSu5GYHZay/f7aAlZt2hBzRgZm9cjOTFwanCHVqVpejO5Z10pBIQAlWyGau2MS7kcPqGtfJ5cpjO4QbkIiknQv7taWgSVDFmjh/HZ/PVRVLRFJLQZM6/ODodgDsKCrhsbHxx8qltpcn7l290uYWsj9KsEL26Jg9ayauOb6zDqsTkQOWm53Fz4Z0jT5/ZMwcVbFEJOXccGIX8nODj54vTVzEorX7nFSQknYUFfPm18ExOrnZxgVHanML2T8lWCGatmwj/566AoBD6tbiimPahxyRiKSr849oQ/tD6gAwccE6PlMVS0RSTPMG+fzw2GCX5N0lziMfpsfxEh9MX8mGbUUAnNyzBU3r5YUckaQ6JVgheiSmenXtCZ2oq+qViByknOwsbtyriqW1WCKSeq47oRP1I5933vp6KbNXbg45ooq9PDH27Kt2IUYi6UIJVki+W7KR0dNXAtC0Xh6XD+gQbkAikvbO69uaDpEq1pcL1vNpoapYIpJaGtWpxTXHdwLAHR7+ILWrWAvXbo3OCGjbuDaDujQNOSJJB0qwQvLImD0/UH4yuDO1a2WHGI2I1ASqYolIOhg+qCOH1K0FwHvTVvDN4g0hR1S+F7/YU726uH8BWVna3EIqpgQrBFMWb+DDmasAaF4/j0u/p3KziCTGuTFVrEkLVcUSkdRTLy+HnwzuHH3+0AezQoymfIvWbuPZzxYAkJ1lfL+/zr6SylGCFYLY6tX1gzuTn6vqlYgkRnwVa4SqWCKSgi4b0J5WDfMB+M+cNUxIwUPS739nGrt2lwBw+YD2tIzEK1IRJVhJ9tWi9YyftRqAlg3yueRoVa9EJLHO7duajk3rAjB54Xo+KVwTckQiInvLz83mZ0P33Ax66P1ZKXUzaMz0lYyZEcw2alqvFrecfGjIEUk6UYKVZLE7B15/oqpXIpJ4QRWrS/S5zsUSkVR0Ub+2e01pLr0BHbYdRcXc98606PM7T+9Bw9q5IUYk6UYJVhJNXriej2cHPzxaNczn4qM0l1dEqsc5h+9dxfrPHFWxRCS15GZn7VUZ+v37sygpCf9m0BPj57J43XYAjurQmAuObBNyRJJulGAl0V5rr07sQl6OqlciUj1ysrP42dDYKpbWYolI6jm7T2u6t6wPwPTlm3jr66WhxrNo7Tae+GguEGxscf+5h2GmnQPlwCjBSpLJC9dF7yC3bpjPsP5tQ45IRGq6s/u0plOkivXVog18rCqWiKSYrCzj9lO6RZ//cuRUCldtCS2e+97ee2OLHq0ahBaLpC8lWEmy99orVa9EpPoFVSydiyUiqW1oj+ac2bsVAFt3FfOT5yezdefupMcxZvrK6DE6TevlaWMLOWhKsJJg0oL46pXWXolIcpx9+J4q1teqYolICjIzHrywN52aBT+r5qzawp1vfpfUG0I7ioq59+09G1vcdUZ3bWwhB00JVhLEVq9+OqQLtXL0bReR5MjOsr2qWCNGq4olIqmnfn4uT17Wj9qR3ZVHfbOMf3y+MGnv/8T4uSxZv2dji/OP0MYWcvD0Sb+afblgXfQMmjaNavP9fqpeiUhynX146+id4SmLN/DR7NTYCllEJNahLerz4IW9o88feHc6kxeur/b3Xbh2qza2kIRSglXNHo2tXp2o6pWIJF92lnHTXmuxdC6WiKSmc/u24cpj2gNQVOzc8OJXrN2ys9rez925d9SejS2uOEYbW0jV6dN+NYqvXl3UTzsHikg4zurTms4xVazxqmIBYGZZZnanmS0wsx1m9o2ZXXgA/c8zs68jfRea2T1mts8uRmY2yMw+M7PtZrbCzB42s9pxbQ4zs6fMbLKZ7TKzcrNgM2tsZs+Y2Roz22pmY8ysd3ntRdLJ3Wf2pG9BIwCWb9zBTS9PobiazscaM2MV4yIHHGtjC0kUJVjVKPbcqxu09kpEQhS/FktVrKhfAfcCjwGnAxOA18zsjIo6mtmpwBvAl5G+jwL3AL+Ja9cHGA2sAs6KtBkO/C3uJfsBZwCLgEn7eV8DRgGnATcCFwK5wDgz0508SXu1crJ4/NIjaVK3FgCfFK7Z6zNVouwoKua+mI0t7j6zOw3ytbGFVJ0+8VeTifPX8WnhWiCoXl14pMY8EQnXWX1a06V5PQC+URULM2sO3A486O4Pufs4d78WGAc8FWa1pQAADYVJREFUWImXeBD4xN2vifR9mCC5usXMWsa0uw9YAnzf3T9092eAm4BhZnZkTLvn3L3A3c8Hxu7nfc8BBgGXu/tL7v5e5FoW8F+V+sOLpLjWjWrzx0uOoHQp1J/GFjJ25sqEvsfjMRtbHN2hCef11cYWkhhKsKqJqlcikmpKq1hZBucf0YaOh9QNO6SwnQrUAp6Pu/480NvMOpbX0cwKgL5l9H2OoJp0eqRdLkGl6VV3L4pp9yqwCzi39IK7l1Qy7nOAZe4+LqbvRuDt2NcTSXeDujbltpgpeze/PIXF67ZV+XXdndcnL+HJ2I0tzuuljS0kYXLCDqAm+mLeWj6bG1Sv2jZW9UpEUseZvVvRu01DOjbN+OQKoBewEyiMu146Z6gnMH8/fQGmxl509/lmti3SF6AzkF9Gux1mNjem3YHGPbWM69OAK8ysnrtvOZAXNLPJpb/v16/fQYQkUj2uH9yFrxZtYOzMVWzasZvrnp/MGz85lvzcfZY6Vsriddu4663voueTAlx5TAe6t9TGFpI4oZZVzKzAzF43s41mtsnM3jSzdpXsm29mvzez5ZFFw5+b2fHVHXNlxJ57dYN2DhSRFJKdZUqu9mgCbPB9F6Oti/n6/voClLWH9PqYr++v3boK3mN/713e6wE0PojXFElJWVnGiGF9ads42BNm2rJN3PbaNyzfuP2AXqe4xHnmP/M4ZcTHeyVXZ/Zuxc9P7ZbQmEVC++RvZnUI5ph3B64ELge6EizSrczo/1fgauCXBIuGlwPvm1nf6om4cibMW8vn82KqV9o5UEQkKczsJDPzSjzGl3YBytrpozLzhErbVNS/su0ORFXiLpO79yt9HOxriFSXhnWCQ4hLb1i/++1yBj44luHPTuS9qSsoKt7/7NpZKzZz4ROf8cC7M9heVAxA8/p5PHlZP/586ZHUrnVw1TCR8oQ5RfBqoBPQzd0LAczsW2AOcC3wcHkdzexw4P8BP3L3ZyPXPiKYHnE/wfz0UMSee3XjkC7kZqt6JSKSJJ8BPSrRrnQRxzqgsZlZXBWrcczXy7O/KlejmK/vr11j9kxHPBDlVb5K467+k1lFkuywNg158ILe/Pz1bykucUocxs1azbhZq2larxYX9mvLxf0L6NSsXrTPzt3F/HncXJ4YX0hR8Z7/4pccVcCdZ/SgYW3tGCjVI8wE6xxgQmlyBdG5658SLNItN8GK9C0CXonpu9vMXgbuMLM8d6++U+nKEVu9KmhSmwu09kpEJGncfRsw8wC6TAPyCNZJxa7DKl0XNb2CvhCsh/q89KKZdQDqxPSdS7DOq1dMX8wsn+Am42sHEG/se59SxvWewKIDXX8lki4uOLIt/ds34dVJi3lt8mJWbgo+6q3ZsounPprHUx/N4+iOTbjkqAJaNazNL0ZOpXDVnv8O7Q+pw28v6M2xnZuG9UeQDBFmeWV/i3QrWvTbC5gfGUzj+9YCulQ9vAMXu3PgjSd2VfVKRCS1vUewk9+lcdcvA6a6e3kbXODui4BvyulbBPw70m5X5H2GmVnsTc2LCJK7UQcR9yigjZmdUHrBzBoAZx/k64mkjXaH1OH2U7vx6X8P4a9X9ufkni3IztozO3bi/HXc+uo3/ODpCdHkKjvLuPaETrx/8/FKriQpwqxg7W+RbkULdCta4HvAi4aruoPS53PXMmFe8PYFTWpz/pE6S0FEJJW5+yozGwHcaWabga+Ai4EhxG13bmYfAu3dPfYG3l3AO2b2FPAScATBIcKPuvuKmHb3ElS5XjWzPwMdgN8Dr7t7dOyJrE0uPeC4e+TaRZHnC9y99PDhUZHXe97Mfk4wHt5JsAbrfw/uuyGSXnKysxjaowVDe7Rg1aYdvP7VEl75cjEL1+59771nqwb870V9OKxNw5AilUwU9jbtVVlcnNAFvlXVsmE+Z/VpxbvfLVf1SkQkfdwNbCE4+LclMAsY5u5vx7XLJm7MdPd/RRKg/wF+CKwkOGj413HtppjZqcDvgHeBjcA/CBK0WM3Zd8pg6fO/R94Ddy8xs7OAh4DHCbaB/xw40d0XV/LPLVJjNG+Qz/WDu3Dd8Z35Yv46XvlyEd8t3ciF/dpy9XGd9JlMks723Z02SW9sthL4p7tfG3f9cYLT7pvtp+8rQF937xZ3fRjBuqzD3P1gFg4D0L9/f580aVLFDcswZ+VmOjStq//MIlJjmdlkd+8fdhxSPaoyBoqI1GSVHf/CzAKmEbfoN6In+19YXNq3Y2Q6RXzfXex7aGTSdG1RX8mViIiIiEiGCjMTGAUMMLNOpRciuy8NpOJFuqOAXOD7MX1zCObOfxDGDoIiIiIiIiJhJlhPAwuAkWZ2rpmdA4wEFgNPlTYys/ZmttvMfll6zd2nEEwFfMTMrjKzocDLQEeCufAiIiIiIiJJF1qC5e5bCXZqmg08B7wAzAeGxJ3hYQSLi+NjHQ48CzxAsGi4ADjN3b+q5tBFRERERETKFOougpFzRC6soM0Cytgd0N23A7dGHiIiIiIiIqHTbgwiIiIiIiIJogRLREREREQkQUI7ByuVmdlqYOFBdO0R+XVGAsORA6O/g3Dp+x+uZH3/2+/vrEJJbxoD05a+/+HS9z98yfg7qNT4pwQrgcxsMoC79ws7lkylv4Nw6fsfLn3/JUz69xcuff/Dpe9/+FLp70BTBEVERERERBJECZaIiIiIiEiCaIqgiIiIiIhIgqiCJSIiIiIikiBKsERERERERBJECZaIiIiIiEiCKMESERERERFJECVYIiIiIiIiCaIES0REREREJEGUYImIiIiIiCSIEiwREREREZEEUYIlIiIiIiKSIEqwREREREREEkQJloiIiIiISIIowUoAMysws9fNbKOZbTKzN82sXdhxZQoza2tmfzKzz81sm5m5mXUIO65MYWYXmdkbZrbQzLab2Swz+62Z1Q87tkxgZqea2VgzW2FmO81siZm9amY9w45NMoPGwHBpDAyPxr/wpeoYaO4e5vunPTOrA3wD7ATuARx4AKgD9HH3rSGGlxHMbDDwCjAZyAZOATq6+4IQw8oYZjYBWASMBJYARwD3AjOBY929JLzoaj4z+wFwJPAFsBpoB9wBFAC93X1hiOFJDacxMHwaA8Oj8S98qToGKsGqIjO7CXgY6ObuhZFrHYE5wH+5+8NhxpcJzCyr9IeYmV0FPI0Gl6Qxs2buvjru2hXA34Gh7j42nMgyl5l1Ixjgb3f3P4Qdj9RcGgPDpzEwPBr/UlMqjIGaIlh15wATSgcWAHefD3wKnBtaVBlEd4jCFT+4RHwZ+bVNMmORqLWRX4tCjUIygcbAkGkMDI/Gv5QV+hioBKvqegFTy7g+DdAaCMlUJ0R+nRFqFBnEzLLNrJaZdQWeAlYAL4ccltR8GgNF9qbxLwSpNgbmhPXGNUgTYH0Z19cBjZMci0jozKwNcD8wxt0nhR1PBvkC6Bf5fSEwxN1XhRiPZAaNgSIRGv9ClVJjoCpYiVHWQjZLehQiITOzegSLfXcDw0MOJ9NcDgwA/h+wCRitncQkSTQGSsbT+Be6lBoDlWBV3XqCO3jxGlP2XT2RGsnM8oFRQCfgVHdfEnJIGcXdZ7j7F+7+EjAUqEewk5JIddIYKBlP41/4Um0M1BTBqptGMAc9Xk9gepJjEQmFmeUCbwBHAye5+3chh5TR3H2DmRUCXcKORWo8jYGS0TT+pZ5UGANVwaq6UcAAM+tUeiFSkhwY+ZpIjWZmWcALBHeMznX3CSGHlPHMrAXQHZgbdixS42kMlIyl8S81pcIYqHOwqsjM6hIcsridPYcs/gqoT3DI4pYQw8sYZnZR5LdDgeuA6wkOnFvt7h+FFlgGMLMnCL7nvwbeifvyEk2VqF5m9hbwFfAtwbzzQ4FbgJbA0e4+O8TwpIbTGJgaNAaGQ+Nf+FJ1DFSClQBm1g4YAZxMsLD3Q+BmHfKXPGZW3j/kj9x9cDJjyTRmtgBoX86X73P3e5MXTeYxs/8GhgGdgVrAYmA88Fv9DJJk0BgYPo2B4dD4F75UHQOVYImIiIiIiCSI1mCJiIiIiIgkiBIsERERERGRBFGCJSIiIiIikiBKsERERERERBJECZaIiIiIiEiCKMESERERERFJECVYIiIiIiIiCaIESySFmVlfM7vXzDqEHYuIiEiyaPyTdKYESyS19QX+B+gQchwiIiLJpPFP0pYSLBERERERkQRRgiWSoszsXuDZyNNxZuaRx73hRSUiIlK9NP5JussJOwARKdebQCvgGuA3wIzI9W9Di0hERKT6afyTtGbuHnYMIlIOM/shwV28E919fLjRiIiIJIfGP0lnmiIoIiIiIiKSIEqwREREREREEkQJloiIiIiISIIowRJJbVokKSIimUjjn6QtJVgiqW1L5NfGoUYhIiKSXBr/JG1pm3aR1DYJKAHuNLPGwDZgqrtPDTcsERGRaqXxT9KWKlgiKczdFwJXAw2Bp4CXgItCDUpERKSaafyTdKZzsERERERERBJEFSwREREREZEEUYIlIiIiIiKSIEqwREREREREEkQJloiIiIiISIIowRIREREREUkQJVgiIiIiIiIJogRLREREREQkQZRgiYiIiIiIJIgSLBERERERkQT5/7DdP+S4iDidAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 864x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from scipy.integrate import solve_bvp\n",
    "\n",
    "plt.style.use('seaborn-poster')\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "F = lambda t, s: np.cos(t)\n",
    "\n",
    "t_eval = np.arange(0, np.pi, 0.1)\n",
    "sol = solve_ivp(F, [0, np.pi], [0], t_eval=t_eval)\n",
    "\n",
    "plt.figure(figsize = (12, 4))\n",
    "plt.subplot(121)\n",
    "plt.plot(sol.t, sol.y[0])\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('S(t)')\n",
    "plt.subplot(122)\n",
    "plt.plot(sol.t, sol.y[0] - np.sin(sol.t))\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('S(t) - sin(t)')\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "button": false,
    "collapsed": true,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [],
   "source": [
    "def fun(t, y):\n",
    "    print(y[1].shape)\n",
    "    return np.vstack((y[1], -9.8))\n",
    "\n",
    "f = lambda t, s: \\\n",
    "  np.dot(np.array([[0,1],[0,-9.8/s[1]]]),s)\n",
    "\n",
    "def bc(ya, yb):\n",
    "    return np.array([ya[0], yb[0]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "button": false,
    "collapsed": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "setting an array element with a sequence.",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-23-2946ad05c3b2>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0my_a\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m=\u001b[0m \u001b[0;36m50\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 6\u001b[0;31m \u001b[0mres_a\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msolve_bvp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbc\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mt\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my_a\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m~/miniconda3/lib/python3.6/site-packages/scipy/integrate/_bvp.py\u001b[0m in \u001b[0;36msolve_bvp\u001b[0;34m(fun, bc, x, y, p, S, fun_jac, bc_jac, tol, max_nodes, verbose)\u001b[0m\n\u001b[1;32m   1053\u001b[0m         fun, bc, fun_jac, bc_jac, k, a, S, D, dtype)\n\u001b[1;32m   1054\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1055\u001b[0;31m     \u001b[0mf\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfun_wrapped\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1056\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1057\u001b[0m         raise ValueError(\"`fun` return is expected to have shape {}, \"\n",
      "\u001b[0;32m~/miniconda3/lib/python3.6/site-packages/scipy/integrate/_bvp.py\u001b[0m in \u001b[0;36mfun_p\u001b[0;34m(x, y, _)\u001b[0m\n\u001b[1;32m    649\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mk\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    650\u001b[0m         \u001b[0;32mdef\u001b[0m \u001b[0mfun_p\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0m_\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 651\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0masarray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    652\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    653\u001b[0m         \u001b[0;32mdef\u001b[0m \u001b[0mbc_wrapped\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mya\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0myb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0m_\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/miniconda3/lib/python3.6/site-packages/numpy/core/numeric.py\u001b[0m in \u001b[0;36masarray\u001b[0;34m(a, dtype, order)\u001b[0m\n\u001b[1;32m    536\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    537\u001b[0m     \"\"\"\n\u001b[0;32m--> 538\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcopy\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0morder\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0morder\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    539\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    540\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mValueError\u001b[0m: setting an array element with a sequence."
     ]
    }
   ],
   "source": [
    "t = np.linspace(0, 5, 11)\n",
    "\n",
    "y_a = np.zeros((2, t.size))\n",
    "y_a[-1]= 50\n",
    "\n",
    "res_a = solve_bvp(f, bc, t, y_a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "button": false,
    "collapsed": true,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [],
   "source": [
    "def fun(x, y):\n",
    "    return np.vstack((y[1], -np.exp(y[0])))\n",
    "\n",
    "def bc(ya, yb):\n",
    "    return np.array([ya[0], yb[0]])\n",
    "\n",
    "x = np.linspace(0, 1, 5)\n",
    "\n",
    "y_a = np.zeros((2, x.size))\n",
    "y_b = np.zeros((2, x.size))\n",
    "#y_b[0] = 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "button": false,
    "collapsed": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/qingkaikong/miniconda3/lib/python3.6/site-packages/ipykernel_launcher.py:6: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  \n",
      "/Users/qingkaikong/miniconda3/lib/python3.6/site-packages/ipykernel_launcher.py:6: RuntimeWarning: invalid value encountered in multiply\n",
      "  \n"
     ]
    },
    {
     "ename": "ValueError",
     "evalue": "setting an array element with a sequence.",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-27-845fe81f85d9>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mres_a\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msolve_bvp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mF\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbc\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my_a\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m~/miniconda3/lib/python3.6/site-packages/scipy/integrate/_bvp.py\u001b[0m in \u001b[0;36msolve_bvp\u001b[0;34m(fun, bc, x, y, p, S, fun_jac, bc_jac, tol, max_nodes, verbose)\u001b[0m\n\u001b[1;32m   1053\u001b[0m         fun, bc, fun_jac, bc_jac, k, a, S, D, dtype)\n\u001b[1;32m   1054\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1055\u001b[0;31m     \u001b[0mf\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfun_wrapped\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1056\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1057\u001b[0m         raise ValueError(\"`fun` return is expected to have shape {}, \"\n",
      "\u001b[0;32m~/miniconda3/lib/python3.6/site-packages/scipy/integrate/_bvp.py\u001b[0m in \u001b[0;36mfun_p\u001b[0;34m(x, y, _)\u001b[0m\n\u001b[1;32m    649\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mk\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    650\u001b[0m         \u001b[0;32mdef\u001b[0m \u001b[0mfun_p\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0m_\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 651\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0masarray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    652\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    653\u001b[0m         \u001b[0;32mdef\u001b[0m \u001b[0mbc_wrapped\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mya\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0myb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0m_\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/miniconda3/lib/python3.6/site-packages/numpy/core/numeric.py\u001b[0m in \u001b[0;36masarray\u001b[0;34m(a, dtype, order)\u001b[0m\n\u001b[1;32m    536\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    537\u001b[0m     \"\"\"\n\u001b[0;32m--> 538\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcopy\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0morder\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0morder\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    539\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    540\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mValueError\u001b[0m: setting an array element with a sequence."
     ]
    }
   ],
   "source": [
    "res_a = solve_bvp(fun, bc, x, y_a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "button": false,
    "collapsed": true,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [],
   "source": [
    "res_b = solve_bvp(fun, bc, x, y_a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "button": false,
    "collapsed": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "       message: 'The algorithm converged to the desired accuracy.'\n",
       "         niter: 1\n",
       "             p: None\n",
       " rms_residuals: array([9.86500717e-05, 1.05360602e-04, 1.05360602e-04, 9.86500717e-05])\n",
       "           sol: <scipy.interpolate.interpolate.PPoly object at 0x1832058938>\n",
       "        status: 0\n",
       "       success: True\n",
       "             x: array([0.  , 0.25, 0.5 , 0.75, 1.  ])\n",
       "             y: array([[ 0.00000000e+00,  1.04784145e-01,  1.40534773e-01,\n",
       "         1.04784145e-01,  0.00000000e+00],\n",
       "       [ 5.49349275e-01,  2.84320977e-01, -1.28752555e-18,\n",
       "        -2.84320977e-01, -5.49349275e-01]])\n",
       "            yp: array([[ 5.49349275e-01,  2.84320977e-01, -1.28752555e-18,\n",
       "        -2.84320977e-01, -5.49349275e-01],\n",
       "       [-1.00000000e+00, -1.11047088e+00, -1.15088910e+00,\n",
       "        -1.11047088e+00, -1.00000000e+00]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res_a.y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "The above figure shows the corresponding numerical results. As in the previous example, the difference between the result of *solve\\_ivp* and the evaluation of the analytical solution by Python is very small in comparison to the value of the function.\n",
    "\n",
    "**EXAMPLE:**\n",
    "\n",
    "Let the state of a system be defined by $S(t) = \\left[\\begin{array}{c} x(t) \\\\y(t) \\end{array}\\right]$, and let the evolution of the system be defined by the ODE\n",
    "\n",
    "$$\n",
    "\\frac{dS(t)}{dt} = \\left[\\begin{array}{cc}\n",
    "0 & t^2 \\\\\n",
    "-t & 0\n",
    "\\end{array}\\right]S(t).\n",
    "$$\n",
    "\n",
    "Use *solve\\_ivp* to solve this ODE for the time interval $[0, 10]$ with an initial value of $S_0 = \\left[\\begin{array}{c} 1 \\\\1 \\end{array}\\right]$. Plot the solution in ($x(t), y(t)$)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "button": false,
    "collapsed": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "F = lambda t, s: np.dot(np.array([[0, t**2], [-t, 0]]), s)\n",
    "\n",
    "t_eval = np.arange(0, 10.01, 0.01)\n",
    "sol = solve_ivp(F, [0, 10], [1, 1], t_eval=t_eval)\n",
    "\n",
    "plt.figure(figsize = (12, 8))\n",
    "plt.plot(sol.y.T[:, 0], sol.y.T[:, 1])\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "In practice, some ODEs have bad behavior known as **stiffness**. Loosely speaking, stiffness refers to systems that can have very sharp changes in derivative. An example of a stiff system is a bouncing ball, which\n",
    "suddenly changes directions when it hits the ground. Depending on the properties of the ODE you are solving and the desired level of accuracy, you might need to use different methods for *solve\\_ivp*. There are many methods that you can choose for the *method* argument in *solve\\_ivp*, take a look of the [documentation](https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.solve_ivp.html#scipy.integrate.solve_ivp) to understand it more. As suggested by the documentation, you should use the 'RK45' or 'RK23' method for non-stiff problems and 'Radau' or 'BDF' for stiff problems. If not sure, first try to run 'RK45'. If needs unusually many iterations, diverges, or fails, your problem is likely to be stiff and you should use 'Radau' or 'BDF'. 'LSODA' can also be a good universal choice, but it might be somewhat less convenient to work with as it wraps old Fortran code."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "<!--NAVIGATION-->\n",
    "< [23.4 Numerical Error and Instability](chapter23.04-Numerical-Error-and-Instability.ipynb) | [Contents](Index.ipynb) | [23.6 Summary and Problems](chapter23.06-Summary-and-Problems.ipynb) >"
   ]
  }
 ],
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