1-radial-light-rays.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
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   "source": [
    "# Exercise 1.1: Radial light rays in Schwarzschild spacetime"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This sample code demonstrates how to numerically integrate an ordinary differential equation in Python."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.integrate import ode"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "def integrate_sample_ode(x0):\n",
    "    t_history = [ 0. ]\n",
    "    x_history = [ x0 ]\n",
    "    x = ode(lambda t, x: x).set_integrator('zvode', method='bdf').set_initial_value(x_history[0], t_history[0])\n",
    "    dt = 0.1\n",
    "    while x.successful() and x.t < 3.:\n",
    "        x_history.append(x.integrate(x.t + dt)[0])\n",
    "        t_history.append(x.t)\n",
    "    return t_history, x_history"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
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   "source": [
    "plt.figure(figsize=(9, 6))\n",
    "for x0 in np.linspace(0., 1., 10):\n",
    "    t, x = integrate_sample_ode(x0=x0)\n",
    "    plt.plot(t, x, marker='.', ls='dotted')"
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  {
   "cell_type": "code",
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   "source": []
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