SecondSession.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "1WNSvEHFpBu8"
   },
   "source": [
    "# Second Session of Stochastic Modelling\n",
    "\n",
    "[![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/guglielmopadula/StochasticModelling2022-2023/blob/main/SecondSession.ipynb)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "iKiYMmrjpecI"
   },
   "source": [
    "## Part 1: A crash course about First Order Ordinary Differential equations and their simulation\n",
    "\n",
    "An first order ordinary differential equation is an equation of the form $$\\begin{cases}y':=\\frac{dy}{dt}=g(y,t) \\\\ y(t_{0})=y_{0}\\end{cases}$$\n",
    "We are going to assume $g\\in C^{\\infty}(\\mathbb{R}^{k},\\mathbb{R})$\n",
    "If $g$ is lipschitz in $y$ so  $$\\left|\\left|\\frac{dg}{dy}(y,t)\\right|\\right|\\le K(t) \\forall t$$  and $$g(t,y)$$ is continuous in $t$ so\n",
    "$$ \\lim \\limits_{t→t_{1}}g(t,y)=g(t_{1},y) \\quad \\forall y,t_{1}\n",
    "$$ \n",
    "then the ODE has an unique solution and so the problem is well defined.\n",
    "We restrict to first order ODE's because ODEs of greater order can be reconducted to first order using change of variables.\n",
    "\n",
    "Some first order ODEs can be solved explicitly, for example given\n",
    "$$\\begin{cases}y'=-yt \\\\ y(0)=1 \\end{cases}$$ we divide by $y$, and multiply by $dt$ to obtain $$\\frac{dy}{y}=-tdt$$, so if we integrate we get $$\\ln(y)=-\\frac{t^{2}}{2}+c$$ or $$y=ce^{-\\frac{t^{2}}{2}}$$\n",
    "By substiting $y(0)=1$ we get $c=1$, so the final solution is $$y=e^{-\\frac{t^{2}}{2}}$$\n",
    "\n",
    "Howewer not all equations can be solved explicitly, for example the equation\n",
    "$$y'=y+sin(y)$$ can't be solved explictly, even if it has a unique solution.\n",
    "\n",
    "So we need numerical methods to simulate their solution.\n",
    "\n",
    "One of the most used are the Finite Difference method, which approximate the derivative.\n",
    "\n",
    "### Forward Euler method\n",
    "\n",
    "We know that $\\lim\\limits _{h \\rightarrow 0}\\frac{y(t+h)-y(t)}{h}=y'(t)$\n",
    "\n",
    "So $$\\lim\\limits _{h \\rightarrow 0}\\frac{y(t+h)-y(t)}{h}=g(t,y)$$ and if $h$ is small we have $$y(t+h)\\approx y(t)+hg(t,y(t))$$\n",
    "So starting from $t_{0}$, supposing we want the value in $t_{e}$ we could choose a number $n$ of intermediate points and discretize our time in $$t_{i}=t_{0}+i\\frac{t_{e}-t_{0}}{n}$$ and do\n",
    "$$y_{i}=y_{i-1}+hg(t_{i-1},y_{i-1})$$ where \n",
    "$$y_{i} \\approx y(t_{i-1})$$\n",
    "\n",
    "This method is called forward euler method. Let's code it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "id": "qvYJE5Z30GXL"
   },
   "outputs": [],
   "source": [
    "def forward_euler(g,t0,t_e,y0,n):\n",
    "  h=(t_e-t0)/n\n",
    "  y=np.zeros(n+1)\n",
    "  y[0]=y0\n",
    "  t=np.linspace(t0,t_e,n+1)\n",
    "  for i in range(1,n+1):\n",
    "    y[i]=y[i-1]+h*g(t[i-1],y[i-1])\n",
    "  return y,t\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "VsQaZo1S3aH5"
   },
   "source": [
    "Now let's test it on our example $y'=-yt$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 283
    },
    "id": "Y40HYnu03kCk",
    "outputId": "4dc2e44a-5f0d-4c50-fa53-1105cf4e01bf"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "L2 error is  0.20177562425048975\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "g= lambda x,t : -x*t\n",
    "y= lambda t: np.exp(-t**2/2)\n",
    "t0=0\n",
    "y0=1\n",
    "t_e=5\n",
    "n=10\n",
    "y_approx,t=forward_euler(g,t0,t_e,y0,n)\n",
    "y_true=y(t)\n",
    "import matplotlib.pyplot as plt\n",
    "plt.plot(t,y_approx)\n",
    "plt.plot(t,y_true)\n",
    "print(\"L2 error is \",np.linalg.norm(y_true-y_approx) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "5Uz3nx1o64Rr"
   },
   "source": [
    "Let's try to increase the number of intermediate points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 283
    },
    "id": "on5XbiS-6ytF",
    "outputId": "7e01f623-c472-4837-e9c0-1c01c3a0d32e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "L2 error is  0.0015192116782519643\n"
     ]
    },
    {
     "data": {
      "image/png": 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YTiQiIsFGZURIGX47+2hBaw6Q84HuOSIiIg1LZURwhUeyo+uxO+i2Wz+d6iq34UQiIhJMVEYEgOQr7+Yg0bS1C1n1n9dMxxERkSCiMiIARDaNYVPS9QDE5kzD6/EYTiQiIsFCZURq9B7xOw7bEXT05rLmk3+ajiMiIkFCZURqRDdrybo2VwMQtvQFw2lERCRYqIzIcTpf8XvctpNeVevYtPwj03FERCQIqIzIcVolJJHTfAgARz95znAaEREJBiojcoK4ofcDkFL+JV9vzjEbRkREAp7KiJygQ/dUVkWeg8OyKVzwlOk4IiIS4FRG5KQiBv8WgNQDCynK32U2jIiIBDSVETmpHgMz2BjamzCrmm3/ftp0HBERCWAqI3JK7rQ7AeiT/y6lh/YbTiMiIoFKZUROqe/gn7PLkUiUdZQN708xHUdERAKUyoicksPppCj51wB03vE3KiuOGE4kIiKBSGVEflDK0FvZRwtacZDV814xHUdERAKQyoj8oDBXODu7jAEgfv0reoCeiIjUOZUR+VG9r7ibUiJp791DzkdvmY4jIiIBRmVEflTT6OZsaHstABErphlOIyIigUZlRGqly7Df4rZD6Fm1gU0rPjYdR0REAojKiNRKbEIHVje/GIDyRVPMhhERkYCiMiK1FnvxvQCkln1K/s5NhtOIiEigUBmRWuvYO4014f1xWja58581HUdERAKEyoj4xEq/A4C++96n5ECx4TQiIhIIVEbEJ33OH8FORxJNrAo2fPBn03FERCQAqIyITyyHg6K+twDQecffcVdWGE4kIiL+TmVEfJYy9GaKaUZrDrB6wWum44iIiJ9TGRGfucIj2ZZ0PQAt1ryC7fUaTiQiIv5MZUROS8/hd3PEdtHZs5P1X/zbdBwREfFjKiNyWmJaxrG21TAAPF+8YDiNiIj4M5UROW1tL/0tXtsipWI5X2/MNh1HRET8lMqInLZ2Xfqwuum5ABT+VzdBExGR06MyImck4oK7AUg9sJDigjzDaURExB+pjMgZ6T4wg80h3Qmzqtn2wfOm44iIiB9SGZEzYjkcHO53GwDdd7/N0fIyw4lERMTfqIzIGUu5+HryrdY0p4w186abjiMiIn5GZUTOWEhoGLldxwCQsPE1vB6P4UQiIuJPVEakTvS5fBylRJJo57Pm49mm44iIiB9RGZE60TS6OevbXA1A6PIXDacRERF/ojIidabTsEyqbCe93WvZmvOZ6TgiIuInVEakzsS168zqmMEAlHw8xWwYERHxGyojUqeaXXQvACkln1CQt81wGhER8QcqI1KnuqScx/qwZEItD7vmPWc6joiI+AGVEalzVYNuB6BXwRwOlx40nEZERBo7lRGpc8mDf06elUA0R1j3wTTTcUREpJFTGZE653A6ye/5SwDab30TT3W14UQiItKYqYxIvUge9hsOEkWCvY/VH/3ddBwREWnEVEakXkQ0iWJTu2sBiFyh59WIiMipqYxIvel6+b247RB6VG9k0/KPTMcREZFGSmVE6k1sfHtyml8CQPnivxhOIyIijdVplZFp06aRlJREeHg4aWlpLFu27AfnHzp0iHHjxtGmTRtcLhfdunVj/vz5pxVY/Euri+8BILXsU/J3bjIbRkREGiWfy8js2bPJzMxk0qRJrFy5kpSUFIYMGcK+fftOOt/tdnPxxReza9cu3nnnHTZv3syMGTNo27btGYeXxq9j7zTWhPfHadnk/kc3QRMRkRNZtm3bvqyQlpbGwIEDmTp1KgBer5fExETuvPNOHnjggRPmT58+naeffppNmzYRGhp6WiFLS0uJiYmhpKSE6Ojo03oNMWfNondJXvRLyu1wqu9ZT0zzWNORRESkAdT289unPSNut5vs7GwyMjK+ewGHg4yMDJYsWXLSdd5//33S09MZN24ccXFx9OnTh8cffxyPx3PK7VRWVlJaWnrcIv6r7wVXscvRniZWBRvnvWA6joiINDI+lZHi4mI8Hg9xcXHHjcfFxVFQUHDSdXbs2ME777yDx+Nh/vz5TJgwgWeffZbHHnvslNuZPHkyMTExNUtiYqIvMaWRsRwOivrcAkDStr9T5a40nEhERBqTer+axuv10rp1a1555RX69+/PyJEjeeihh5g+/dT3nhg/fjwlJSU1S15eXn3HlHrWd+gt7CeGeIpZ/d83TccREZFGxKcyEhsbi9PppLCw8LjxwsJC4uPjT7pOmzZt6NatG06ns2asZ8+eFBQU4Ha7T7qOy+UiOjr6uEX8W3hEE7a0HwVATM4r2F6v4UQiItJY+FRGwsLC6N+/P1lZWTVjXq+XrKws0tPTT7rOueeey7Zt2/B+78Nny5YttGnThrCwsNOMLf6o++V3UWGH0rV6KxuXLjQdR0REGgmfD9NkZmYyY8YM3nzzTTZu3Mhtt91GeXk5Y8eOBWD06NGMHz++Zv5tt93GgQMHuPvuu9myZQvz5s3j8ccfZ9y4cXX3W4hfaNG6LatbDgWg8jPdBE1ERI4J8XWFkSNHUlRUxMSJEykoKCA1NZUFCxbUnNSam5uLw/Fdx0lMTGThwoXce++9JCcn07ZtW+6++27uv//+uvstxG/ED/ktvPU+KeVLyNu2lsQufU1HEhERw3y+z4gJus9IYFn95CWkHF3K0tirSbvjddNxRESkntTLfUZE6oLzvDsBSC76gJL9hT8yW0REAp3KiDS43unD2O7sRITlZsMHfzYdR0REDFMZkQZnORwcSL4VgC47Z1JZedRwIhERMUllRIxIufSX7KMFrTjI6v+8ZjqOiIgYpDIiRoS5wtne8ToAYtfoJmgiIsFMZUSM6TX8Ho7YLjp5d7H+i3+bjiMiIoaojIgxMS1asbbV5QB4vpxqOI2IiJiiMiJGtb00E69tkXJ0Gbs2rTQdR0REDFAZEaPadenD6qbnAlC48DnDaURExASVETEu/IK7AEg9sID9+/YYTiMiIg1NZUSM6zHwYraEdMNlVbHlgymm44iISANTGRHjLIeDsrN+DUD33FlUHC03nEhERBqSyog0CimXjKaAVrSglDXzXzEdR0REGpDKiDQKIaFh7Op6IwBx61/VTdBERIKIyog0Gr2G3cFhO4IO3jzWLP6X6TgiItJAVEak0Yhu1pJ18VcC4PhKN0ETEQkWKiPSqHS4LBOPbdG3chXb1y41HUdERBqAyog0Km06dCcn6icAHPhIN0ETEQkGKiPS6ET99F4AUg59SHH+14bTiIhIfVMZkUanW78L2RjaizDLw9Z5z5uOIyIi9UxlRBqligG3AdBzzz85crjEcBoREalPKiPSKCVfdB17rDiacZi18142HUdEROqRyog0Ss6QEHZ3vwmAhE2v4/V4zAYSEZF6ozIijVafYbdTShMS7XzWfDzbdBwREaknKiPSaDWJasaGhJ8BELr8RcNpRESkvqiMSKPW6bJ7qbKd9HavZWvOZ6bjiIhIPVAZkUatdbtOrI75KQAlWVPMhhERkXqhMiKNXrOLvrkJWuknFORtM5xGRETqmsqINHpdUs5lfVgKoZaHXfN0i3gRkUCjMiJ+oTrtdgB6FczhcOlBw2lERKQuqYyIX+h74bXkOtoSzRHWfTDVdBwREalDKiPiFxxOJ3t73gxA0pY3qHJXGk4kIiJ1RWVE/EbK5b+hmGbEU0zO/L+ajiMiInVEZUT8RnhEE7Z2Gg1A7JrpukW8iEiAUBkRv9L7insosyPo6M1lzSdvm44jIiJ1QGVE/Ep0s5asS7gWgPClf8a2bcOJRETkTKmMiN/pOvw+Ku1QelRtZOPS/5qOIyIiZ0hlRPxObEIHcloOBaBq8bOG04iIyJlSGRG/1Pay+/HYFilHl7Jj3VLTcURE5AyojIhfatelDzlRPwFg/3+fNpxGRETOhMqI+K2Yi38HwFklWeTv2mw4jYiInC6VEfFbXVLOY62rHyGWl9x5T5mOIyIip0llRPyadf69AKTse58D+/YYTiMiIqdDZUT8Wu9zLmdrSFciLDdb3teVNSIi/khlRPya5XBQNuAOAHrunsXhskNmA4mIiM9URsTvpWTcQK6VQAzlrHv/L6bjiIiIj1RGxO85Q0Io6PMrADptfZ3KiiOGE4mIiC9URiQgpAz7NftoQWsOkPPvl0zHERERH6iMSEBwhUeyo9stACRumE6Vu9JwIhERqS2VEQkYKVfexX5iSLD3sWr+X03HERGRWlIZkYAR0SSKrZ3GANBm9VQ81dWGE4mISG2ojEhA6TMik0M0JdHOZ9XCN0zHERGRWlAZkYDSNLo5GzvcAEDL7L/g9XgMJxIRkR+jMiIBp9eI31FmR9DR+zU5WW+ZjiMiIj9CZUQCTkzzWNa1GwlA1NLnsb1ew4lEROSHqIxIQOp+5f0csV109WxjzeJ/mY4jIiI/4LTKyLRp00hKSiI8PJy0tDSWLVtWq/VmzZqFZVmMGDHidDYrUmstWiewJv5qAFxfPqO9IyIijZjPZWT27NlkZmYyadIkVq5cSUpKCkOGDGHfvn0/uN6uXbu47777OP/88087rIgvulw5nko7lB5VG1m/ZL7pOCIicgo+l5HnnnuOW2+9lbFjx9KrVy+mT59OZGQkr7322inX8Xg8XH/99TzyyCN06tTpjAKL1FZsQgdyWg0/9s3ip82GERGRU/KpjLjdbrKzs8nIyPjuBRwOMjIyWLJkySnX++Mf/0jr1q25+eaba7WdyspKSktLj1tETkeHKx7EbTvp485h47IPTccREZGT8KmMFBcX4/F4iIuLO248Li6OgoKCk67z+eef8+qrrzJjxoxab2fy5MnExMTULImJib7EFKkR374rOS2GAlCd9bjhNCIicjL1ejVNWVkZN954IzNmzCA2NrbW640fP56SkpKaJS8vrx5TSqBrd+VEqmwnfStXsuGrBabjiIjI/wjxZXJsbCxOp5PCwsLjxgsLC4mPjz9h/vbt29m1axfDhw+vGfN+c1VDSEgImzdvpnPnzies53K5cLlcvkQTOaWEpO4sjb2ctP3vYX/8OJx9qelIIiLyPT7tGQkLC6N///5kZWXVjHm9XrKyskhPTz9hfo8ePVi7di05OTk1yxVXXMHgwYPJycnR4RdpMB2unIDbdtLbvZr1X8wzHUdERL7Hpz0jAJmZmYwZM4YBAwYwaNAgpkyZQnl5OWPHjgVg9OjRtG3blsmTJxMeHk6fPn2OW79Zs2YAJ4yL1Kf49l1Z2upK0or/hbV4Mnb6UCyH7vknItIY+FxGRo4cSVFRERMnTqSgoIDU1FQWLFhQc1Jrbm4uDv2Rl0YoacTDVM74N73ca1n35Qf0Oe8K05FERASwbNu2TYf4MaWlpcTExFBSUkJ0dLTpOOLHlk67mbSid9gY2ose47/Q3hERkXpU289v/SWWoNL5qglU2KH0rNrAus/mmo4jIiKojEiQiU1IIifu2DNrQj97Us+sERFpBFRGJOh0ufphjtph9KjexJrF75qOIyIS9FRGJOjExrdndZtrAIj8QntHRERMUxmRoNTtqoc4YrvoWr2V1VmzTMcREQlqKiMSlFrEtWNN25EAxCx5Ak91teFEIiLBS2VEglbPaydSShM6er9m5bxXTMcREQlaKiMStGKat2JDx18C0DbnedyVFYYTiYgEJ5URCWop19xPEc1JsPexas7zpuOIiAQllREJahFNotjR63YAumx6ifKyQ2YDiYgEIZURCXr9RtzNbiuelpSw5p0nTMcREQk6KiMS9ELDXBT0ywSgz643OFRcYDiRiEhwURkRAfpddgs7nElEWUfZ+M4fTccREQkqKiMigMPppOzchwA4a+/bFO7ZYTiRiEjwUBkR+UbyhdewMbQ34VYVu96ZaDqOiEjQUBkR+YblcGBl/AGAAQc+YNfGFWYDiYgECZURke/pkXYJq5qch9OyKXl/vOk4IiJBQWVE5H/EjphMle0k5egy1n76nuk4IiIBT2VE5H8kdk0mu/XVAEQunqSH6ImI1DOVEZGT6P7zRyklks6enWT/+yXTcUREAprKiMhJNG/Vhg2dbwUgafVzHC0vM5xIRCRwqYyInELqNfeTb7WmNQfIefsx03FERAKWyojIKYRHNCF/wO8BSNn1OsUFuYYTiYgEJpURkR/Qf+jNbAnpRqRVyfZ/Pmw6johIQFIZEfkBlsOB5+Jjh2gGFL/PjnVLDScSEQk8KiMiP6Jn2hBWNr0Ap2Vz9P37sL1e05FERAKKyohILbS59hkq7FB6u9ewcsGbpuOIiAQUlRGRWmjToTur2o8FoO2yx3Spr4hIHVIZEaml1F9MpIBWxFNMzqxHTMcREQkYKiMitRTRJIr8tIcAOCv3DfJ3bTacSEQkMKiMiPjgrCFjWBeWQrhVxd5/3mc6johIQFAZEfGB5XDQ5Mqn8dgW/cs/Zd3n75uOJCLi91RGRHzUsXcaK1ode6pv048foqrKbTiRiIh/UxkROQ09Rk3mIFEkeXPJnj3ZdBwREb+mMiJyGmJaxrE1+XcAJG+dRkHeNsOJRET8l8qIyGkacOUdbAztTaRVSf5bd5uOIyLit1RGRE6Tw+nEddUUqmwn/Y58zqqP3jIdSUTEL6mMiJyBTr0GsSLhOgDiP5/AkcMlhhOJiPgflRGRM5Ry/Z/YSyvaUMTqfzxkOo6IiN9RGRE5Q5FNYyg871EABuTPZOeG5YYTiYj4F5URkTqQmjGKVZHnEmp5qJhzF16Px3QkERG/oTIiUkfajPoLR2wXPas2sPydZ0zHERHxGyojInUkPrELa3rcA0CfDc+x92s9SE9EpDZURkTq0KCf38/G0F40sSooeut2bK/XdCQRkUZPZUSkDjmcTiKveYlKO5TkihWseP9F05FERBo9lRGROtaheyorO/0agG45j1NckGs4kYhI46YyIlIPBlw3iW3OzsRQTu7fxpmOIyLSqKmMiNSD0NAwGDHt2K3iyz9l5X9eNx1JRKTRUhkRqSdd+qazot0YAJKWTmR/4W7DiUREGieVEZF61O/GP7HTkUQLSsl781ZdXSMichIqIyL1yBUeifeql3HbTlKPfMmKuS+YjiQi0uiojIjUs859zya787GTWHutfpz8nZsMJxIRaVxURkQawKDrJrExtDdNrAoOvXUznupq05FERBoNlRGRBuAMCSF61KscsV30cq9j+Vt/NB1JRKTRUBkRaSBtO/VkXd8HAOi3bRo71y81nEhEpHFQGRFpQAOvvofVEWcTZlXjePdmjh4uNR1JRMS40yoj06ZNIykpifDwcNLS0li2bNkp586YMYPzzz+f5s2b07x5czIyMn5wvkggsxwO2t30KsU0o4M3j7Wv3WY6koiIcT6XkdmzZ5OZmcmkSZNYuXIlKSkpDBkyhH379p10/qJFixg1ahSffPIJS5YsITExkUsuuYQ9e/accXgRf9Qyrh2FF/0Fr20x6MAHZM/7q+lIIiJGWbZt276skJaWxsCBA5k6dSoAXq+XxMRE7rzzTh544IEfXd/j8dC8eXOmTp3K6NGja7XN0tJSYmJiKCkpITo62pe4Io3Wkhn3kL7ndcrsCErHfELbTj1NRxIRqVO1/fz2ac+I2+0mOzubjIyM717A4SAjI4MlS5bU6jWOHDlCVVUVLVq0OOWcyspKSktLj1tEAs3Am55iY2gvoqyjlM8cjbuywnQkEREjfCojxcXFeDwe4uLijhuPi4ujoKCgVq9x//33k5CQcFyh+V+TJ08mJiamZklMTPQlpohfCAkNo/mN/0cpTehWvYWVr2eajiQiYkSDXk3zxBNPMGvWLObMmUN4ePgp540fP56SkpKaJS8vrwFTijSc+PZd2Zb+FABnF/yDVf/9u+FEIiINz6cyEhsbi9PppLCw8LjxwsJC4uPjf3DdZ555hieeeIL//ve/JCcn/+Bcl8tFdHT0cYtIoOo35Aa+aj0SgC5f3Efe1jWGE4mINCyfykhYWBj9+/cnKyurZszr9ZKVlUV6evop13vqqad49NFHWbBgAQMGDDj9tCIBqv8tL7AxtDdR1lE8b13PkcMlpiOJiDQYnw/TZGZmMmPGDN588002btzIbbfdRnl5OWPHjgVg9OjRjB8/vmb+k08+yYQJE3jttddISkqioKCAgoICDh8+XHe/hYifCw1z0WrsWxTTjCRvLhtfvgnb6zUdS0SkQfhcRkaOHMkzzzzDxIkTSU1NJScnhwULFtSc1Jqbm8vevXtr5r/00ku43W6uueYa2rRpU7M888wzdfdbiASA2IQOFA19hSrbSf+yj1k2+3HTkUREGoTP9xkxQfcZkWDy1czHOHvL01TZTrZd+g96pg81HUlE5LTUy31GRKT+pf3iQbKjfkqo5SF+4a/I37nJdCQRkXqlMiLSyFgOB71+839sc3amOaW4/3YtZSUHTMcSEak3KiMijVBEkyiixv6TIpqT5M1lx/SReKqrTccSEakXKiMijVRcu84cvOJNKuxQUo4uY/mMO0xHEhGpFyojIo1Yt34/YX3akwCcXfgWy96dYjaQiEg9UBkRaeT6X3YzSxJvBeCsNX9k7aJ3DScSEalbKiMifuDssU+xIjqDUMtD509uY1vOZ6YjiYjUGZURET9gORwkj/sH61ypRFqVNJ97PXt2bDQdS0SkTqiMiPiJMFc4HW6fw3ZnR1pSgvdvV3Ng3x7TsUREzpjKiIgfiYppQfTNc9lLKxLtfIpfGaGH6omI31MZEfEzrRKScI96h0M0pVv1Fra/cCUVR8tNxxIROW0qIyJ+qEP3VAou/z+O2C76Vq5i01+uxl1ZYTqWiMhpURkR8VM9BlzEzktep8IOJfXoV6x74edUV7lNxxIR8ZnKiIgf633uMLZcOB237aTf4cWsmnoDXo/HdCwREZ+ojIj4ueTB17D+3L9QbTsYWLKQFdPGqJCIiF9RGREJAGddcgM5A5/EY1sMOvBvsl+4Tg/WExG/oTIiEiAGXP4rVg186tgekkMLyPmLziEREf+gMiISQAZc/ivWpD9Ple2kf2kWa/78M6rcuspGRBo3lRGRANPv0ptYf/403HYI/Q5/yvopI6g4cth0LBGRU1IZEQlAqRmj2HThy8cu+z2yhJ3PX0LJgSLTsURETkplRCRAJQ++hh2X/o1SIulZtZ6DU39K4e5tpmOJiJxAZUQkgPVKH8r+a+eyjxYkeXPhr5fw9cZs07FERI6jMiIS4Dr2TsP7y4V87WhHHPtpNns467+cbzqWiEgNlRGRIBDfvhsxt2exKaQnMZTTbeENLHt3iulYIiKAyohI0GgWG09S5kdkRw0m1PIwaO0kvnrp17o5mogYpzIiEkTCI5vS795/saT9rwE4u3AW65+5lNJD+w0nE5FgpjIiEmQsh4P0Xz5F9qApHLXDSK5YTsmfz2PXhuWmo4lIkFIZEQlS/S8by+6r/kUhLUm082k9exgr3n/JdCwRCUIqIyJBrGvq+YTe/hlrXf2ItCoZsPIBlr4wmoqj5aajiUgQURkRCXItWrel1+8+ZEnirXhti7T975H3zAXkbVtrOpqIBAmVERHBGRJC+s3PsO7Cv3KIpnT1bKPl3y5i2TvPYXu9puOJSIBTGRGRGsmDr6Hylk9Z50ol0qpk0LpHWP3MMA7s22M6mogEMJURETlOXLvO9Pr9x3zV5V7cdgipR77E++I5rP7oLdPRRCRAqYyIyAkcTidn3/AH8q6Zx05He2I5RMrnvyH72RHsL9xtOp6IBBiVERE5pc59z6bN775iSZsbqLYd9C/7BOdLaax4b5rOJRGROqMyIiI/KDyiCem/nsbOq/7NdmcnmnGYAaseZO1TGeRtXW06nogEAJUREamVrqnn0f7+r1jScRyVdijJFdnE/X0wS14ex+HSg6bjiYgfUxkRkVoLDXORPuZxCm/4mNURgwizPKTv/TsVz6Wy/L0X8Xo8piOKiB9SGRERn7XvmkzK/R+y+oKX2W21IZZDDFw1nm2Tz2bd5++bjicifkZlREROW8pPf0Gr+1eypNOdlNvhdKveQp+PbmTt5MFszfnMdDwR8ROWbdu26RA/prS0lJiYGEpKSoiOjjYdR0ROorhwN9ve+QP99v2LMOvY4ZqVTX9C88sm0LHXQMPpRMSE2n5+q4yISJ3K37mJPXMn0P/QhzisY39eVkWeS5OM++nW7yeG04lIQ1IZERGjdq5fysH/PEZq2Wc1pWStqx/WBb+ld/plWA4dJRYJdCojItIofL15FfvmP8FZh/5LiHXsRmnbnZ040Psm+l56M+GRTQ0nFJH6ojIiIo1K/q7N5H4wmZSieURYbgAOEsWmhKvpOPQu4hO7GE4oInVNZUREGqWS/YVsnD+NpO0ziacIAI9tsS5iAJ6U6+k9eCSu8EjDKUWkLqiMiEijVl3lZs3Hs3Flv0Jv95qa8UM0ZVOrobQ6/5d06nO2zi0R8WMqIyLiN/K2rWX3J3+l8573ac2BmvGvHe3Ib3spbc4ZRVLPAQYTisjpUBkREb/jqa5m3Wdzqc7+P/qUfYnLqqr52S5HInvbDaXVwKvp3DtNe0xE/IDKiIj4tbKSA2xe/DbOTXPpXb6cMKu65meFtGRXi3Nx9RxKt/RhRDaNMZhURE5FZUREAkbJof1sWTSbkC3v0718JZFWZc3PKu1QtkQkU55wLi36XESnvucQEhpmMK2IfEtlREQCUsXRcrZ89R+OrJ9P+/2fkWDvO+7nZXYEOyKTqWh7Di16/5Sk3oMIDQs3lFYkuKmMiEjAs71ecjevYu+q/+Da/QWdj6wmmvLj5lTYoewK68qhFimEdRhEQp/ziWvXWeeciDQAlRERCTqe6mp2rPuK4nUfEbHnSzoeXUfM/5QTgGKakR/emSPNehCS0JeWnfvRrmsqoWEuA6lFApfKiIgEPdvrZff2tRSs/wLv7uW0OLiGpOqdhH7zVOHvc9tO8kLac6hJJ9zNOhPWuhsxiT2J79ibptHNDaQX8X8qIyIiJ3G0vIzcjcs5tCsHCtYSXbKZdu4dRFlHT7lOEc3ZF5ZIeZNEPNGJhDRPpEnrjjRr05lWbTtqj4rIKdRrGZk2bRpPP/00BQUFpKSk8MILLzBo0KBTzv/nP//JhAkT2LVrF127duXJJ5/ksssuq/X2VEZEpD7ZXi97c7dSuHUFlXs34Ti4najDu2hdtZuWlPzguh7bothqwYHQOI66WuGOaI3dtDXO6HhczdrQpEUCzVon0iy2DSGhoQ30G4k0DrX9/A7x9YVnz55NZmYm06dPJy0tjSlTpjBkyBA2b95M69atT5j/5ZdfMmrUKCZPnszll1/OzJkzGTFiBCtXrqRPnz6+bl5EpM5ZDgcJSd1JSOp+ws9KDhZTuHMdJXkbqN6/i5DS3YQfzaeZu5DW3iJcVhVx7Ceuaj9UAYfhm0fuHMdjW+y3ojnsiOKIM5rKkBiqwmLwhDfDDm+GI7IFzqYtcEW1xNW0Ba7IaMKbxhDRtBlNmsbgDPH5z7WI3/B5z0haWhoDBw5k6tSpAHi9XhITE7nzzjt54IEHTpg/cuRIysvL+eCDD2rGzj77bFJTU5k+fXqttqk9IyLSGHk9Hg4U7WH/7m2U79tFVUk+dlkhziNFuCqKaVK1nxjPAZrbJTitMzsiftQO44gVwVErgkpHJJWOSKpCIql2RuJ1uvCGhGM7Xdgh4RASjhUSDqHhOELDsUIjcIZF4AiLwBkaQagrAkdoGA5nKM7QMJwhoThDXDhDQwkJDSPkm/GQb5eQUF19JKelXvaMuN1usrOzGT9+fM2Yw+EgIyODJUuWnHSdJUuWkJmZedzYkCFDmDt37im3U1lZSWXldzc1Ki0t9SWmiEiDcDidxMa3Jza+/Q/O81RXU1ScT2nRXipKi3EfLqbq8AE85Qfg6EEcFYcIdZcQVlVCZHUJEd5yIjhKpH2UsG9Oto2w3ETgBrsEPBxbqn5ws3WqynZSzTeLFYIHJ14ceHFgY2Fb333ttRzYHFu8lnXsa+ubn+HE/v7YN+N8sz7fHwPAAuvY18fGrJrhb7+2vzcHrP/5/nvzrO+tf8Lrfjv8zRzrZK/1/Xn1Uc6sH59SM7X2c+1avm77Yb876d7BhuBTGSkuLsbj8RAXF3fceFxcHJs2bTrpOgUFBSedX1BQcMrtTJ48mUceecSXaCIijZYzJIRW8e1p9SOl5X/Ztk1FxVGOHi7h6OESKspLcJeX4D5SStXRMrwVpXgqy7GrK6CqAqorsKorsDyVOKorcHgrcXgqcXorCfG4CbErCfW6CbUrcdrVOPEQQjUheAixv/kXD46T7MUJtTyEcuJVSN+FPcXX4jc2FY/yjzLSUMaPH3/c3pTS0lISExMNJhIRaXiWZREeEUl4RCTNW7VpsO16qqupqqqkusqNt6qKqupKPFVVVFe58VS78Va7qa6qwrY94PXi9XqwbQ+214vX6wWv59iY1wZvNV7bC7YH2+PF/vZrrxfb6zn2vfeb720v2MfGsW3A/uZfTvm1/SM/P+XXtv1dZ7K9fNugLBtsvDVzanyb53/Hf1Tt5lo+vKbtS9vz4XU7xnWo/evWMZ/KSGxsLE6nk8LCwuPGCwsLiY+PP+k68fHxPs0HcLlcuFy6VE5ExARnSMixE2YjmpiOIkHCp4NeYWFh9O/fn6ysrJoxr9dLVlYW6enpJ10nPT39uPkAH3744Snni4iISHDx+TBNZmYmY8aMYcCAAQwaNIgpU6ZQXl7O2LFjARg9ejRt27Zl8uTJANx999385Cc/4dlnn2XYsGHMmjWLFStW8Morr9TtbyIiIiJ+yecyMnLkSIqKipg4cSIFBQWkpqayYMGCmpNUc3NzcXzvErBzzjmHmTNn8vDDD/Pggw/StWtX5s6dq3uMiIiICKDbwYuIiEg9qe3nt+5iIyIiIkapjIiIiIhRKiMiIiJilMqIiIiIGKUyIiIiIkapjIiIiIhRKiMiIiJilMqIiIiIGKUyIiIiIkb5fDt4E769SWxpaanhJCIiIlJb335u/9jN3v2ijJSVlQGQmJhoOImIiIj4qqysjJiYmFP+3C+eTeP1esnPzycqKgrLsursdUtLS0lMTCQvL0/PvKlHep8bjt7rhqH3uWHofW4Y9fk+27ZNWVkZCQkJxz1E93/5xZ4Rh8NBu3bt6u31o6Oj9R+9Aeh9bjh6rxuG3ueGofe5YdTX+/xDe0S+pRNYRURExCiVERERETEqqMuIy+Vi0qRJuFwu01ECmt7nhqP3umHofW4Yep8bRmN4n/3iBFYREREJXEG9Z0RERETMUxkRERERo1RGRERExCiVERERETEqqMvItGnTSEpKIjw8nLS0NJYtW2Y6UsD59NNPGT58OAkJCViWxdy5c01HCjiTJ09m4MCBREVF0bp1a0aMGMHmzZtNxwpIL730EsnJyTU3h0pPT+c///mP6VgB7YknnsCyLO655x7TUQLOH/7wByzLOm7p0aOHkSxBW0Zmz55NZmYmkyZNYuXKlaSkpDBkyBD27dtnOlpAKS8vJyUlhWnTppmOErAWL17MuHHj+Oqrr/jwww+pqqrikksuoby83HS0gNOuXTueeOIJsrOzWbFiBT/96U+58sorWb9+veloAWn58uW8/PLLJCcnm44SsHr37s3evXtrls8//9xIjqC9tDctLY2BAwcydepU4NjzbxITE7nzzjt54IEHDKcLTJZlMWfOHEaMGGE6SkArKiqidevWLF68mAsuuMB0nIDXokULnn76aW6++WbTUQLK4cOH6devHy+++CKPPfYYqampTJkyxXSsgPKHP/yBuXPnkpOTYzpKcO4ZcbvdZGdnk5GRUTPmcDjIyMhgyZIlBpOJnLmSkhLg2Iek1B+Px8OsWbMoLy8nPT3ddJyAM27cOIYNG3bc32mpe1u3biUhIYFOnTpx/fXXk5ubaySHXzwor64VFxfj8XiIi4s7bjwuLo5NmzYZSiVy5rxeL/fccw/nnnsuffr0MR0nIK1du5b09HQqKipo2rQpc+bMoVevXqZjBZRZs2axcuVKli9fbjpKQEtLS+ONN96ge/fu7N27l0ceeYTzzz+fdevWERUV1aBZgrKMiASqcePGsW7dOmPHfYNB9+7dycnJoaSkhHfeeYcxY8awePFiFZI6kpeXx913382HH35IeHi46TgBbejQoTVfJycnk5aWRocOHXj77bcb/LBjUJaR2NhYnE4nhYWFx40XFhYSHx9vKJXImbnjjjv44IMP+PTTT2nXrp3pOAErLCyMLl26ANC/f3+WL1/On//8Z15++WXDyQJDdnY2+/bto1+/fjVjHo+HTz/9lKlTp1JZWYnT6TSYMHA1a9aMbt26sW3btgbfdlCeMxIWFkb//v3JysqqGfN6vWRlZenYr/gd27a54447mDNnDh9//DEdO3Y0HSmoeL1eKisrTccIGBdddBFr164lJyenZhkwYADXX389OTk5KiL16PDhw2zfvp02bdo0+LaDcs8IQGZmJmPGjGHAgAEMGjSIKVOmUF5eztixY01HCyiHDx8+rmXv3LmTnJwcWrRoQfv27Q0mCxzjxo1j5syZvPfee0RFRVFQUABATEwMERERhtMFlvHjxzN06FDat29PWVkZM2fOZNGiRSxcuNB0tIARFRV1wvlOTZo0oWXLljoPqo7dd999DB8+nA4dOpCfn8+kSZNwOp2MGjWqwbMEbRkZOXIkRUVFTJw4kYKCAlJTU1mwYMEJJ7XKmVmxYgWDBw+u+T4zMxOAMWPG8MYbbxhKFVheeuklAC688MLjxl9//XVuuummhg8UwPbt28fo0aPZu3cvMTExJCcns3DhQi6++GLT0UR8tnv3bkaNGsX+/ftp1aoV5513Hl999RWtWrVq8CxBe58RERERaRyC8pwRERERaTxURkRERMQolRERERExSmVEREREjFIZEREREaNURkRERMQolRERERExSmVEREREjFIZEREREaNURkRERMQolRERERExSmVEREREjPp/q/DBRkGwJXQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n=100000\n",
    "y_approx,t=forward_euler(g,t0,t_e,y0,n)\n",
    "y_true=y(t)\n",
    "plt.plot(t,y_approx)\n",
    "plt.plot(t,y_true)\n",
    "print(\"L2 error is \",np.linalg.norm(y_true-y_approx) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "L21BT51iGkA0"
   },
   "source": [
    "Much better.\n",
    "\n",
    "Howewer this method has it's drawbacks. Consider $$\\begin{cases} y'=y+e^{2x} \\\\ y(0)=1\\end{cases}$$\n",
    "\n",
    "The solution is $e^{2x}$. Let's pretend we don't know it and let's try to apply the euler algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 321
    },
    "id": "rumR35pPMVms",
    "outputId": "de6fd98b-b7a3-4d55-8669-3be9ddcb938e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "L2 error is  inf\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_5201/3828521638.py:2: RuntimeWarning: overflow encountered in exp\n",
      "  g= lambda x,t : x+np.exp(2*t)\n"
     ]
    },
    {
     "data": {
      "image/png": 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xY4aCwaDGjh0rSRo/frzy8vI0efJkLV68WKFQSHPmzFFJSYnS09Pb6W31DNEzU1CYJAsAsE7Sk2Qv5plnnpHX69XEiRNVV1enwsJCLVu2zN2fkpKiDRs2aNq0aQoGg+rXr5+Ki4s1f/789u6K9aLxCkoKAQUAYBeP4zReTMMg4XBYfr9ftbW1PXo+yoSf/kb7Pwrr5//vZn3p2kFd3R0AAC4omfGb7+IxWHyZcSpzUAAAliGgGCw+SdZLQAEAWIaAYrDGAgoVFACAdQgoBqOCAgCwFQHFYPELtVFBAQDYhoBiMLeCwnVQAACWIaAYLMql7gEAliKgGCx+oTY+4gEA2IaAYrBo4zIeJskCAGxDQDFYlAu1AQAsRUAxWLTxWwqYJAsAsA0BxWBuBYUvCwQAWIaAYrB4QEmhggIAsAwBxVCO47iXumeZMQDANgQUQ8WrJxIBBQBgHwKKoeITZCUCCgDAPgQUQ1FBAQDYjIBiKAIKAMBmBBRDJQQUVvEAACxDQDEUFRQAgM0IKIZyv4fHI3mooAAALENAMVR8FQ/VEwCAjQgohopECSgAAHsRUAwVc7jMPQDAXgQUQ0ViVFAAAPYioBgqRkABAFiMgGKosxUUfoQAAPswuhkq6gaULu4IAAAdgOHNUPFJsqlUUAAAFmJ0M1T8Ix7yCQDARgxvhopPkqWCAgCwEaOboSJNLnUPAIBtCCiGYpkxAMBmBBRDscwYAGAzRjdDnf2ywC7uCAAAHYDhzVDRKBUUAIC9GN0M5VZQmIICALAQAcVQUZYZAwAsxuhmqCgXagMAWIzhzVBUUAAANmN0M9TZCgqTUAAA9iGgGOpsBYWAAgCwDwHFUPFVPF4PAQUAYB8CiqGooAAAbEZAMVSU7+IBAFiMgGIoJskCAGxGQDEUH/EAAGyWVEBZvny5Ro0aJZ/PJ5/Pp2AwqE2bNrn7T58+rZKSEg0cOFD9+/fXxIkTVV1dnfAcVVVVKioqUt++fZWVlaVZs2YpEom0z7vpQZgkCwCwWVIB5YorrtCiRYtUWVmp3/3ud7rzzjt1zz33aO/evZKkmTNn6pVXXtH69eu1detWHT16VPfdd597fDQaVVFRkerr67Vt2zatWbNGq1ev1ty5c9v3XfUAVFAAADbzOE7jf8XbKDMzUz/+8Y91//33a9CgQVq7dq3uv/9+SdKBAwc0YsQIVVRUaOzYsdq0aZO+9rWv6ejRowoEApKkFStWaPbs2fr444+VlpbWqtcMh8Py+/2qra2Vz+e7lO4ba0n5+/rJlvf09ZuHaOF9I7u6OwAAXFQy43eb56BEo1GtW7dOp06dUjAYVGVlpRoaGlRQUOC2GT58uIYMGaKKigpJUkVFhUaOHOmGE0kqLCxUOBx2qzAtqaurUzgcTrj1dBEqKAAAiyUdUPbs2aP+/fsrPT1d3/nOd/TSSy8pLy9PoVBIaWlpysjISGgfCAQUCoUkSaFQKCGcxPfH953PwoUL5ff73Vtubm6y3bZOjGXGAACLJR1QrrvuOu3evVs7duzQtGnTVFxcrH379nVE31xlZWWqra11b0eOHOnQ1zNBhIACALBYarIHpKWl6eqrr5YkjR49Wrt27dJPf/pTPfjgg6qvr1dNTU1CFaW6ulrZ2dmSpOzsbO3cuTPh+eKrfOJtWpKenq709PRku2q1mENAAQDY65KvgxKLxVRXV6fRo0erV69eKi8vd/cdPHhQVVVVCgaDkqRgMKg9e/bo2LFjbpstW7bI5/MpLy/vUrvSo0SiBBQAgL2SqqCUlZVpwoQJGjJkiE6cOKG1a9fqrbfe0muvvSa/368pU6aotLRUmZmZ8vl8mjFjhoLBoMaOHStJGj9+vPLy8jR58mQtXrxYoVBIc+bMUUlJCRWSJLkVFK6DAgCwUFIB5dixY/rmN7+pjz76SH6/X6NGjdJrr72mr3zlK5KkZ555Rl6vVxMnTlRdXZ0KCwu1bNky9/iUlBRt2LBB06ZNUzAYVL9+/VRcXKz58+e377vqAfguHgCAzS75OihdgeugSGW/2qNf7KxS6Veu1fe+fE1XdwcAgIvqlOugoGuxzBgAYDMCiqFYZgwAsBkBxVBMkgUA2IyAYigqKAAAmxFQDMUcFACAzQgohorEYpIIKAAAOxFQDBU9k08IKAAAKxFQDBWlggIAsBgBxVCNX8XDKh4AgJUIKIaKV1BSUwgoAAD7EFAMFf8uHi8VFACAhQgohooHlFTmoAAALERAMZRbQSGgAAAsREAxVHySLBUUAICNCCiGik+SpYICALARAcVQ7oXamCQLALAQAcVQ7jJjKigAAAsRUAzFJFkAgM0IKIZimTEAwGYEFENFHSooAAB7EVAMFY1SQQEA2IuAYii3gsIqHgCAhQgohnLnoPBlgQAACxFQDBUPKFwHBQBgIwKKoSLxgMIcFACAhQgohooRUAAAFiOgGCo+SZaAAgCwEQHFUFEqKAAAixFQDMUkWQCAzQgoBnIcR435hAoKAMBKBBQDxasnEgEFAGAnAoqBIgQUAIDlCCgGijkEFACA3QgoBqKCAgCwHQHFQLGmAYVVPAAACxFQDEQFBQBgOwKKgeIVFK9H8lBBAQBYiIBioHgFJdXLjw8AYCdGOAPFr4NCPgEA2IohzkDxZcZUUAAAtmKEM1CkyRwUAABsREAxUIxvMgYAWI6AYqCIG1D48QEA7MQIZ6CoG1C6uCMAAHQQhjgDRVlmDACwHCOcgaIOy4wBAHZjiDMQFRQAgO2SGuEWLlyoL37xixowYICysrJ077336uDBgwltTp8+rZKSEg0cOFD9+/fXxIkTVV1dndCmqqpKRUVF6tu3r7KysjRr1ixFIpFLfzc9RJRlxgAAyyUVULZu3aqSkhJt375dW7ZsUUNDg8aPH69Tp065bWbOnKlXXnlF69ev19atW3X06FHdd9997v5oNKqioiLV19dr27ZtWrNmjVavXq25c+e237uyHBUUAIDtPI7jOBdv1rKPP/5YWVlZ2rp1q770pS+ptrZWgwYN0tq1a3X//fdLkg4cOKARI0aooqJCY8eO1aZNm/S1r31NR48eVSAQkCStWLFCs2fP1scff6y0tLSLvm44HJbf71dtba18Pl9bu2+st9/7WN/82U6NGOzTpu/f1tXdAQCgVZIZvy/pv+C1tbWSpMzMTElSZWWlGhoaVFBQ4LYZPny4hgwZooqKCklSRUWFRo4c6YYTSSosLFQ4HNbevXtbfJ26ujqFw+GEW092toLCZzwAADu1OaDEYjE98sgjGjdunG644QZJUigUUlpamjIyMhLaBgIBhUIht03TcBLfH9/XkoULF8rv97u33NzctnbbCme/LJCAAgCwU5sDSklJif7v//5P69ata8/+tKisrEy1tbXu7ciRIx3+mt1ZhAoKAMByqW05aPr06dqwYYPefvttXXHFFe727Oxs1dfXq6amJqGKUl1drezsbLfNzp07E54vvson3qa59PR0paent6WrVop/m3GKh4ACALBTUhUUx3E0ffp0vfTSS3rzzTc1bNiwhP2jR49Wr169VF5e7m47ePCgqqqqFAwGJUnBYFB79uzRsWPH3DZbtmyRz+dTXl7epbyXHuPsRzxd3BEAADpIUhWUkpISrV27Vv/93/+tAQMGuHNG/H6/+vTpI7/frylTpqi0tFSZmZny+XyaMWOGgsGgxo4dK0kaP3688vLyNHnyZC1evFihUEhz5sxRSUkJVZJWYpkxAMB2SQWU5cuXS5L+9m//NmH7qlWr9K1vfUuS9Mwzz8jr9WrixImqq6tTYWGhli1b5rZNSUnRhg0bNG3aNAWDQfXr10/FxcWaP3/+pb2THoRJsgAA2yUVUFpzyZTevXtr6dKlWrp06XnbDB06VBs3bkzmpdEEy4wBALbjMwIDuV8WyCRZAIClCCgGYpkxAMB2BBQDxRoDSgoBBQBgKQKKgSIEFACA5QgoBqKCAgCwHQHFQFRQAAC2I6AYiEvdAwBsR0AxUCTaGFBSCCgAADsRUAwUpYICALAcAcVATJIFANiOgGIgJskCAGxHQDGQO0mWgAIAsBQBxUDuJFkCCgDAUgQUA7HMGABgOwKKgSKxmCQqKAAAexFQDBQ9k08IKAAAaxFQDBSlggIAsBwBxUBUUAAAtiOgGCheQUkloAAALEVAMVDjKmN5WcUDALAUAcVAbgWFLwsEAFiKgGKgaOOl7qmgAABsRUAxUJTv4gEAWI6AYiACCgDAdgQUA8UnyXKpewCArQgoBmKSLADAdgQUAzFJFgBgOwKKgeIBhQu1AQBsRUAxkFtBIaAAACxFQDEQFRQAgO0IKAaKOlRQAAB2I6AYKBKlggIAsBsBxUCxxgoK10EBANiKgGKgCFeSBQBYjoBioBgBBQBgOQKKgaigAABsR0AxEBUUAIDtCCgGcpcZM0kWAGApAoqB3Au18WWBAABLEVAMFA8oLDMGANiKgGIgJskCAGxHQDEQk2QBALYjoBiICgoAwHYEFAO5l7onoAAALEVAMRAVFACA7QgohonFHDUWUFjFAwCwFgHFMPGLtElSqpcfHwDATkmPcG+//bbuvvtu5eTkyOPx6OWXX07Y7ziO5s6dq8GDB6tPnz4qKCjQ+++/n9Dm+PHjmjRpknw+nzIyMjRlyhSdPHnykt5ITxG/BookkU8AALZKeog7deqUPv/5z2vp0qUt7l+8eLGWLFmiFStWaMeOHerXr58KCwt1+vRpt82kSZO0d+9ebdmyRRs2bNDbb7+tqVOntv1d9CBNAwoVFACArVKTPWDChAmaMGFCi/scx9Gzzz6rOXPm6J577pEk/fznP1cgENDLL7+shx56SPv379fmzZu1a9cujRkzRpL03HPP6a677tLTTz+tnJycS3g79mv6EQ/5BABgq3Yd4g4fPqxQKKSCggJ3m9/vV35+vioqKiRJFRUVysjIcMOJJBUUFMjr9WrHjh0tPm9dXZ3C4XDCraeKRs8GFCbJAgBs1a4BJRQKSZICgUDC9kAg4O4LhULKyspK2J+amqrMzEy3TXMLFy6U3+93b7m5ue3ZbaM0raCwzBgAYCsjPiQoKytTbW2tezty5EhXd6nLxC9z7/VIHiooAABLtWtAyc7OliRVV1cnbK+urnb3ZWdn69ixYwn7I5GIjh8/7rZpLj09XT6fL+HWU8Uv0sYEWQCAzdp1lBs2bJiys7NVXl7ubguHw9qxY4eCwaAkKRgMqqamRpWVlW6bN998U7FYTPn5+e3ZHSvFV/GQTwAANkt6Fc/Jkyf1wQcfuI8PHz6s3bt3KzMzU0OGDNEjjzyip556Stdcc42GDRumxx9/XDk5Obr33nslSSNGjNBXv/pVPfzww1qxYoUaGho0ffp0PfTQQ6zgaYUoFRQAQA+QdED53e9+pzvuuMN9XFpaKkkqLi7W6tWr9cMf/lCnTp3S1KlTVVNTo1tvvVWbN29W79693WNefPFFTZ8+XV/+8pfl9Xo1ceJELVmypB3ejv3ik2SZHwsAsJnHcZosCzFEOByW3+9XbW1tj5uP8l71CY1/5m1l9kvT7x//Sld3BwCAVktm/OZzAsO4c1BYwQMAsBgBxTBn56AQUAAA9iKgGCYeULhIGwDAZgQUw0QIKACAHoCAYpiYQ0ABANiPgGKYSJRlxgAA+xFQDBOvoHChNgCAzRjlDHP2UveUUAAA9iKgGIZlxgCAnoCAYhgqKACAnoCAYpgIFRQAQA9AQDGMu8yYS90DACxGQDEMF2oDAPQEBBTDxAgoAIAegIBiGCooAICegIBiGCooAICegIBiGCooAICegIBimCireAAAPQABxTDRaEwSFRQAgN0IKIZp/DJjAgoAwGoEFMNEY1RQAAD2I6AYpvETHgIKAMBqBBTDcKl7AEBPQEAxTKRxEkpKCgEFAGAvAophWGYMAOgJCCiGYZIsAKAnIKAYhkmyAICegIBimHgFJZWAAgCwGAHFMPEKipeAAgCwGAHFMFRQAAA9AQHFMPFVPF5W8QAALEZAMUw01rjMmAoKAMBiBBTDEFAAAD0BAcUwEQIKAKAHIKAYJtYYUJgkCwCwGQHFMI1fxcMkWQCA1QgohnGXGfNlgQAAixFQDBOfJEsFBQBgMwKKYaLMQQEA9AAEFMO4FRQCCgDAYgQUw0SooAAAegACimFiDtdBAQDYj4BimEiUgAIAsB8BxTBuBYVVPAAAixFQDBNhkiwAoAdI7eoOIDlc6h4A0CqOI8WiUqxBijZIsciZW4v3G6RopEnbBsn3OSlrRJd1n4BiGCooANBKsZjkRBsH4Gjj/SaPY5Em26JnB22n2ePmx7S2TYuPz7ftAvuj8fsNifujDS0HkPg+J3pp52/M/5O+9kz7/CzaoEsDytKlS/XjH/9YoVBIn//85/Xcc8/p5ptv7soudUsN0Zh++8EnemX3Ub1/7KQkKiiAsRxHcmKNA2as8db0vtNkX7SFtrFm2+JtWmrfOIg6TpP7sQvsa9Ymvq3p/VishfbRJv1u4blavT2WOPgnvF7zkBFttj3WrE2kq3/S3Ze3l5TSS/Kmnrmdc7+XlJIq+XK6tJtdFlD+8z//U6WlpVqxYoXy8/P17LPPqrCwUAcPHlRWVlZXdatTxWKO/toQ1an6iP5aH9WpuqhOnG7QX07V65OTdfrkZL3+/Olf9eaBan36WYN73JWD+un6HH8X9txCjnPmppb+jJ3nfpM/E+7HkngeXeD5L/C68ddp+lot3o9Jji6wr6XHF2vTdJuabGuy/XzPec7zNDumxddqbZuW2remTVtvjs4NDtFzn7t5Gzkd+lcZreRJOTsoe1MkjzfxsTelWZtUyett9rixjTvAt/DYm5pkm+av2UKIOGdf/H7j8W7bXon7UnqdeZ+GLLLwOI7TJf9a8vPz9cUvflH/+q//KkmKxWLKzc3VjBkz9Oijj17w2HA4LL/fr9raWvl8vnbr04Edr6vmd7+U5DSOBY4cOXIaf8Ge2dR4v/EXUHxbfHushftO0/uxmKKOIyd25rk9chT/q+Jp9lhNHvdO9Sjb11uD/b2V0Sc1oU3iQNjStpb2Nbvf6ue40J/NjjvneZN8jqa/zFsVHs7X7/OEiuZ9BboTj7fJLT5gNg4u52yLP25y3+M9OxjGj3EfexOPbWn7OduaPb+7rXmb82x3A8DF2qdefFtLx57TJrVJn1sII4YM0rZJZvzukgpKfX29KisrVVZW5m7zer0qKChQRUXFOe3r6upUV1fnPg6Hwx3Sr9qq/9XYj9d3yHMn8EhKSfIYR1Jt4w0G8DT5Jdj8fuNjd3tL7Zu38bTQPv74fO3i95U4SDXd7z5uaVtLbeLP47lImyav7w5qzV/rfNvix6UktmnxeZq/VorOOS/nPE9r2jQb6BNey5t4fPzY5s/T9JiLtUnY1vQ8AD1XlwSUTz75RNFoVIFAIGF7IBDQgQMHzmm/cOFC/ehHP+rwfmVc9UVVfPotebweeRp/AXo8njO/370eeeRt/N3scW9er0cez5ntXq9X3vh2j0der1cpXq88Xo9SPB6leL1KSTmzLTXlzONeqSnq1fgcZ38hNR0AmvySim9rer/FP5s9xzntlXi/Nc/RqjatOaY1f7b2eZoN6C29r6aDWfM/z9nn1YXPyXkG5HOel4EFAC6VEat4ysrKVFpa6j4Oh8PKzc1t99e57qbbpZtub/fnBQAAyemSgHL55ZcrJSVF1dXVCdurq6uVnZ19Tvv09HSlp6d3VvcAAEAX65IryaalpWn06NEqLy93t8ViMZWXlysYDHZFlwAAQDfSZR/xlJaWqri4WGPGjNHNN9+sZ599VqdOndK3v/3truoSAADoJrosoDz44IP6+OOPNXfuXIVCId14443avHnzORNnAQBAz9Nl10G5FB11HRQAANBxkhm/+TZjAADQ7RBQAABAt0NAAQAA3Q4BBQAAdDsEFAAA0O0QUAAAQLdDQAEAAN0OAQUAAHQ7RnybcXPxa8uFw+Eu7gkAAGit+LjdmmvEGhlQTpw4IUnKzc3t4p4AAIBknThxQn6//4JtjLzUfSwW09GjRzVgwAB5PJ52fe5wOKzc3FwdOXKEy+h3IM5z5+A8dw7Oc+fgPHeejjrXjuPoxIkTysnJkdd74VkmRlZQvF6vrrjiig59DZ/Pxz+ATsB57hyc587Bee4cnOfO0xHn+mKVkzgmyQIAgG6HgAIAALodAkoz6enpmjdvntLT07u6K1bjPHcOznPn4Dx3Ds5z5+kO59rISbIAAMBuVFAAAEC3Q0ABAADdDgEFAAB0OwQUAADQ7RBQAABAt9MjA8rSpUv1N3/zN+rdu7fy8/O1c+fOC7Zfv369hg8frt69e2vkyJHauHFjJ/XUbMmc55UrV+q2227TZZddpssuu0wFBQUX/bngjGT/PsetW7dOHo9H9957b8d20BLJnueamhqVlJRo8ODBSk9P17XXXsvvjlZI9jw/++yzuu6669SnTx/l5uZq5syZOn36dCf11kxvv/227r77buXk5Mjj8ejll1++6DFvvfWWbrrpJqWnp+vqq6/W6tWrO7yfcnqYdevWOWlpac7PfvYzZ+/evc7DDz/sZGRkONXV1S22f+edd5yUlBRn8eLFzr59+5w5c+Y4vXr1cvbs2dPJPTdLsuf5G9/4hrN06VLn3Xffdfbv3+9861vfcvx+v/Phhx92cs/Nkux5jjt8+LDzuc99zrntttuce+65p3M6a7Bkz3NdXZ0zZswY56677nJ++9vfOocPH3beeustZ/fu3Z3cc7Mke55ffPFFJz093XnxxRedw4cPO6+99pozePBgZ+bMmZ3cc7Ns3LjReeyxx5xf/epXjiTnpZdeumD7Q4cOOX379nVKS0udffv2Oc8995yTkpLibN68uUP72eMCys033+yUlJS4j6PRqJOTk+MsXLiwxfYPPPCAU1RUlLAtPz/f+cd//McO7afpkj3PzUUiEWfAgAHOmjVrOqqLVmjLeY5EIs4tt9zi/Pu//7tTXFxMQGmFZM/z8uXLnSuvvNKpr6/vrC5aIdnzXFJS4tx5550J20pLS51x48Z1aD9t0pqA8sMf/tC5/vrrE7Y9+OCDTmFhYQf2zHF61Ec89fX1qqysVEFBgbvN6/WqoKBAFRUVLR5TUVGR0F6SCgsLz9sebTvPzX322WdqaGhQZmZmR3XTeG09z/Pnz1dWVpamTJnSGd00XlvO869//WsFg0GVlJQoEAjohhtu0IIFCxSNRjur28Zpy3m+5ZZbVFlZ6X4MdOjQIW3cuFF33XVXp/S5p+iqcdDIbzNuq08++UTRaFSBQCBheyAQ0IEDB1o8JhQKtdg+FAp1WD9N15bz3Nzs2bOVk5Nzzj8KnNWW8/zb3/5WL7zwgnbv3t0JPbRDW87zoUOH9Oabb2rSpEnauHGjPvjgA333u99VQ0OD5s2b1xndNk5bzvM3vvENffLJJ7r11lvlOI4ikYi+853v6J//+Z87o8s9xvnGwXA4rL/+9a/q06dPh7xuj6qgwAyLFi3SunXr9NJLL6l3795d3R1rnDhxQpMnT9bKlSt1+eWXd3V3rBaLxZSVlaXnn39eo0eP1oMPPqjHHntMK1as6OquWeWtt97SggULtGzZMv3+97/Xr371K7366qt68sknu7praAc9qoJy+eWXKyUlRdXV1Qnbq6urlZ2d3eIx2dnZSbVH285z3NNPP61FixbpjTfe0KhRozqym8ZL9jz/4Q9/0B//+Efdfffd7rZYLCZJSk1N1cGDB3XVVVd1bKcN1Ja/z4MHD1avXr2UkpLibhsxYoRCoZDq6+uVlpbWoX02UVvO8+OPP67JkyfrH/7hHyRJI0eO1KlTpzR16lQ99thj8nr5P3h7ON846PP5Oqx6IvWwCkpaWppGjx6t8vJyd1ssFlN5ebmCwWCLxwSDwYT2krRly5bztkfbzrMkLV68WE8++aQ2b96sMWPGdEZXjZbseR4+fLj27Nmj3bt3u7e/+7u/0x133KHdu3crNze3M7tvjLb8fR43bpw++OADNwBK0nvvvafBgwcTTs6jLef5s88+OyeExEOhw/fgtpsuGwc7dApuN7Ru3TonPT3dWb16tbNv3z5n6tSpTkZGhhMKhRzHcZzJkyc7jz76qNv+nXfecVJTU52nn37a2b9/vzNv3jyWGbdCsud50aJFTlpamvNf//VfzkcffeTeTpw40VVvwQjJnufmWMXTOsme56qqKmfAgAHO9OnTnYMHDzobNmxwsrKynKeeeqqr3oIRkj3P8+bNcwYMGOD84he/cA4dOuS8/vrrzlVXXeU88MADXfUWjHDixAnn3Xffdd59911HkvOTn/zEeffdd50//elPjuM4zqOPPupMnjzZbR9fZjxr1ixn//79ztKlS1lm3FGee+45Z8iQIU5aWppz8803O9u3b3f33X777U5xcXFC+1/+8pfOtdde66SlpTnXX3+98+qrr3Zyj82UzHkeOnSoI+mc27x58zq/44ZJ9u9zUwSU1kv2PG/bts3Jz8930tPTnSuvvNL5l3/5FycSiXRyr82TzHluaGhwnnjiCeeqq65yevfu7eTm5jrf/e53nU8//bTzO26Q//mf/2nx92383BYXFzu33377OcfceOONTlpamnPllVc6q1at6vB+ehyHOhgAAOheetQcFAAAYAYCCgAA6HYIKAAAoNshoAAAgG6HgAIAALodAgoAAOh2CCgAAKDbIaAAAIBuh4ACAAC6HQIKAADodggoAACg2/n/bgAabqxhVh4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "g= lambda x,t : x+np.exp(2*t)\n",
    "y= lambda t: np.exp(2*t)\n",
    "t0=0\n",
    "y0=1\n",
    "t_e=1\n",
    "n=100\n",
    "y_approx,t=forward_euler(g,t0,t_e,y0,n)\n",
    "y_true=y(t)\n",
    "import matplotlib.pyplot as plt\n",
    "plt.plot(t,y_approx)\n",
    "plt.plot(t,y_true)\n",
    "print(\"L2 error is \",np.linalg.norm(y_true-y_approx) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "3iLTHVdlqZs9"
   },
   "source": [
    "It does not work very well. Let's try to increase the points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 331
    },
    "id": "Cqn7RY2qqZ-8",
    "outputId": "7afdc55a-eca8-4be1-ffba-e6914f353b1f"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_5201/3828521638.py:2: RuntimeWarning: overflow encountered in exp\n",
      "  g= lambda x,t : x+np.exp(2*t)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "L2 error is  inf\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n=10000\n",
    "y_approx,t=forward_euler(g,t0,t_e,y0,n)\n",
    "y_true=y(t)\n",
    "import matplotlib.pyplot as plt\n",
    "plt.plot(t,y_approx)\n",
    "plt.plot(t,y_true)\n",
    "print(\"L2 error is \",np.linalg.norm(y_true-y_approx) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "3FDifZpNqFF3"
   },
   "source": [
    "The problem get's worse. Why? The problem is that the exponential magnifies the error."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "OXxywzZ4tTEq"
   },
   "source": [
    "For our luck, there exists much more advanced solvers (which use more than one point at a time). One is in scipy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 283
    },
    "id": "XST7be1btl-J",
    "outputId": "34b55572-f3ca-40a4-b1de-a9d8091f6a5b"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "L2 error is  25279.751914650307\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.integrate import odeint\n",
    "n=10000\n",
    "t=np.linspace(t0,t_e,n)\n",
    "y_approx=odeint(g,y0,t)\n",
    "y_true=y(t)\n",
    "plt.plot(t,y_approx)\n",
    "plt.plot(t,y_true)\n",
    "print(\"L2 error is \",np.linalg.norm(y_true-y_approx) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Pp2cut2uuQr5"
   },
   "source": [
    "It wooooorks!!!!!!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "19IshpQrpusP"
   },
   "source": [
    "## Part 2: Continous Dynamical Systems and their simulation\n",
    "A continuos dinamical system is described by and ode $\\dot{X}=g(X,t)$.\n",
    "\n",
    "If $g$ depends only on $X$ the dynamical system is called autonomous.\n",
    "In this case the solutions of $g(X)=0$ are called equilibrium points of the system and are indicated with $X_{e}$.\n",
    "If:\n",
    "- $g'(X_{e})< 0$ then the points is an attractive/stable equilibrium point (it exists an enough small perturbation such that the system returns to the equilibrium point)\n",
    "- $g'(X_{e})> 0$ then the point is an unstable equilibrium point (it does not exists an enough small perturbation such that the system returns to the equilibrium point)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "TobjR738FYIP"
   },
   "source": [
    "The Gizburg Landau equation is $\\dot{X}=aX-X^{3}=g(X)$\n",
    "\n",
    "The zeros of $g$ are $x=0$ ($\\forall a$ ), $x=-\\sqrt{a}$, $x=\\sqrt{a}$ (only if $a>0$). \n",
    "\n",
    "Also $g'(0)=a$, $g'(-\\sqrt{a})=g'(\\sqrt{a})=-a$.\n",
    "\n",
    "So:\n",
    "- if $a>0$ $x_{1}=0$ is an unstable point and $x_{2}=\\sqrt{a}$ and\n",
    " $x_{3}=-\\sqrt{a}$ are locally stable points\n",
    "- if $a<0$ $x_{1}=0$ is globally stable point\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 279
    },
    "id": "XtcQrSNiE8hU",
    "outputId": "5373d6ff-82e5-4a10-b193-07e5fea2c848"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import scipy\n",
    "import numpy as np\n",
    "from math import sqrt\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "class DynamicalSystem1D(object):\n",
    "  def __init__(self):\n",
    "      super().__init__()\n",
    "\n",
    "  def ode(x,t):\n",
    "    pass\n",
    "  \n",
    "  def solve(self,x0,t):\n",
    "    return scipy.integrate.odeint(self.ode,x0,t)\n",
    "\n",
    "  def plot(self,xlist,t):\n",
    "    \n",
    "    for x0 in xlist:\n",
    "      x=self.solve(x0,t)\n",
    "      plt.plot(t,x)\n",
    "    plt.xlabel(\"Time\")\n",
    "    plt.ylabel(\"X\")\n",
    "\n",
    "class ginzburg_landau(DynamicalSystem1D):\n",
    "  def __init__(self,a):\n",
    "    super().__init__()\n",
    "    self.a=a\n",
    "\n",
    "  def ode(self,x,t):\n",
    "    return self.a*x-x**3\n",
    "\n",
    "  def plot(self,x0,t):\n",
    "    super().plot(x0,t)\n",
    "\n",
    "a=1\n",
    "\n",
    "ginzburg_landau(a).plot([3,-3,0,0.01,-0.01,sqrt(a),-sqrt(a)],np.arange(500)/100)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 279
    },
    "id": "KjxOWSj-oGQD",
    "outputId": "b4afb0d8-fd26-4f02-ef1b-9f17a089ebb1"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a=-1\n",
    "ginzburg_landau(a).plot([3,-3,0.01,-0.01,0],np.arange(500)/100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "r0o2Hdj_FYDK"
   },
   "source": [
    "Notice that if the derivative is 0, then nothing can be said, as the next two examples show"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "id": "bARvtV8_ggTj"
   },
   "outputs": [],
   "source": [
    "class SimplePositiveSquaredDS(DynamicalSystem1D):\n",
    "  def __init__(self):\n",
    "    super().__init__()\n",
    "\n",
    "  def ode(self,x,t):\n",
    "    return x**2\n",
    "\n",
    "  def plot(self,x0,t):\n",
    "    super().plot(x0,t)\n",
    "        \n",
    "    \n",
    "class SimplePositiveCubicDS(DynamicalSystem1D):\n",
    "  def __init__(self):\n",
    "    super().__init__()\n",
    "\n",
    "  def ode(self,x,t):\n",
    "    return x**3\n",
    "\n",
    "  def plot(self,x0,t):\n",
    "    super().plot(x0,t)\n",
    "    \n",
    "    \n",
    "class SimpleNegativeCubicDS(DynamicalSystem1D):\n",
    "  def __init__(self):\n",
    "    super().__init__()\n",
    "\n",
    "  def ode(self,x,t):\n",
    "    return -x**3\n",
    "\n",
    "  def plot(self,x0,t):\n",
    "    super().plot(x0,t)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "PS=SimplePositiveSquaredDS()\n",
    "PS.plot([-0.01,0],np.arange(50000)/100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "PS=SimplePositiveSquaredDS()\n",
    "PS.plot([0.01,0],np.arange(5000)/100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "PS=SimplePositiveCubicDS()\n",
    "PS.plot([0.1,-0.1,0],np.arange(500)/100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "PS=SimpleNegativeCubicDS()\n",
    "PS.plot([0.1,-0.1,0],np.arange(500000)/100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "colab": {
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.16"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}