{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Define right hand side in u'=f(t,u)\n",
    "def f(t,u):\n",
    "    return sin(u)-t*u"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Set initial time, initial value for u(0), final time, and stepsize \"h\".\n",
    "init_time = 0.0\n",
    "initu = 1.0\n",
    "finaltime = 5.0\n",
    "h = 0.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Load in Euler's method subroutine, execute\n",
    "load('euler_method.sage')\n",
    "euler_results = euler_method(f,[init_time,initu],h,finaltime)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Load in improved Euler method subroutine, execute\n",
    "load('imp_euler.sage')\n",
    "impeuler_results = imp_euler(f,[init_time,initu],h,finaltime)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Load in RK4 routine, execute\n",
    "load('rk4_method.sage')\n",
    "rk4_results = rk4_method(f,[init_time,initu],h,finaltime)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Plot results for each solver\n",
    "p1 = line(euler_results,rgbcolor=[1,0,0],legend_label='Euler method')\n",
    "p2 = line(impeuler_results,rgbcolor=[0,1,0],legend_label='Improved Euler')\n",
    "p3 = line(rk4_results,rgbcolor=[0,0,0],legend_label='RK4')\n",
    "p = p1+p2+p3\n",
    "p.set_legend_options(loc='upper center');\n",
    "p.axes_labels(['$t$','$u(t)$'])\n",
    "show(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "SageMath 9.2",
   "language": "sage",
   "name": "sagemath"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}