{ "cells": [ { "cell_type": "markdown", "id": "81b1d2f0", "metadata": {}, "source": [ "---\n", "title: \"P1\"\n", "subtitle: \"Problem Class 1: Initial Value Problems\"\n", "abstract: \"Exercises based on content from Lectures 1-4\"\n", "date: 2026-02-04\n", "format:\n", " html:\n", " other-links:\n", " - text: This notebook\n", " href: P1.ipynb\n", "---" ] }, { "cell_type": "code", "execution_count": 3, "id": "db6fe346", "metadata": {}, "outputs": [], "source": [ "#| echo: false\n", "\n", "using Plots, LaTeXStrings, OrdinaryDiffEq" ] }, { "cell_type": "markdown", "id": "e2f3ac8a", "metadata": {}, "source": [ "Make sure we are all happy with the examples/exercises from lectures 1-4.\n", "\n", "::: {#exr-1}\n", "\n", "Consider the problem: $u : [0,T] \\to \\mathbb R$\n", "\n", "\\begin{align}\n", " u(0) &= u_0 \\nonumber\\\\\n", " u'(t) &= f\\big( t, u(t) \\big). \\tag{IVP}\n", "\\end{align}\n", "\n", "For each of the following functions $f$ and time intervals $[0,T]$ does $(\\text{IVP})$ has a unique solution?\n", "\n", "* *(i)* $f(t, u) = t^2 \\sin u$ and $T = 1$, \n", "* *(ii)* $f(t, u) = \\sqrt[3]{u}$ and $T = 5$, \n", "* *(iii)* $f(t, u) = \\mu u$, $T = 2026$. \n", "\n", ":::\n", "\n", "::: {#exr-2}\n", "\n", "Explain why the IVP \n", "\n", "\\begin{align}\n", " u(0) &= 1 \\nonumber\\\\\n", " u'(t) &= u(t) + e^{-t} \n", "\\end{align}\n", "\n", "has a unique solution for all time. Compute the solution using the integrating factor. \n", "\n", ":::\n", "\n", "\n", "::: {#exr-3}\n", "\n", "Here, we plot solutions to \n", "\n", "\\begin{align}\n", " u(0) &= u_0 \\nonumber\\\\\n", " u'(t) &= \\cos u(t) \n", "\\end{align}\n", "\n", "for different choices of initial values $u_0$. " ] }, { "cell_type": "code", "execution_count": 96, "id": "b82aeb0d", "metadata": {}, "outputs": [ { "data": { "image/png": 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ylabel=L\"u(t)\")\n", "\n", "for u0 = vcat(0:.1:2π, [π/2,π,3π/2,2π])\n", " ivp = ODEProblem(f, u0, tspan)\n", " sol = solve(ivp, Tsit5()); \n", " plot!(sol,\n", " label=\"u0 = $u0\",\n", " xlabel=L\"t\", ylabel=L\"u(t)\")\n", "end\n", "display(P)" ] }, { "cell_type": "markdown", "id": "6a6b59f1", "metadata": {}, "source": [ "\n", "What are the possible values $\\alpha$ for which $u(t) \\to \\alpha$ as $t\\to\\infty$. Do all solutions have limits for large $t$? \n", "\n", "Now add the term $\\sin t$ and consider \n", "\n", "\\begin{align}\n", " u(0) &= u_0 \\nonumber\\\\\n", " u'(t) &= \\cos u(t) + \\sin t.\n", "\\end{align}\n", "\n", "What do you expect to happen to the solutions? Change the code above to find out - was your hypothesis correct?\n", "\n", ":::\n", "\n", "::: {#exr-4}\n", "\n", "Show that the following IVP is well-posed\n", "\n", "\\begin{align}\n", " u(0) &= 0 \\nonumber\\\\\n", " u'(t) &= t + u(t). \n", "\\end{align}\n", "\n", "Compute the first few terms of Euler's method. Show that Euler's method generates the sequence \n", "\n", "\\begin{align}\n", " u_j = (1 + h)^j - ( 1 + jh ).\n", "\\end{align}\n", "\n", "Check that the exact solution is given by $u(t) = e^t - t- 1$. Hence, prove an error bound for $|u(t_j) - u_j|$ and compare with the error bound obtained from the Theorem from lectures.\n", "\n", ":::\n", "\n", "::: {#exr-5}\n", "\n", "Write down the method that corresponds to the Butcher tableau:\n", "\n", "\\begin{array}\n", "{c|cccc}\n", "0\\\\\n", "c & a \\\\\n", "\\hline\n", "& 0 & b\n", "\\end{array}\n", "\n", ":::\n", "\n", "::: {#exr-6}\n", "\n", "Consider the IVP\n", "\n", "\\begin{align}\n", " u(0) &= 1 \\nonumber\\\\\n", " u'(t) &= u(t).\n", "\\end{align}\n", "\n", "Compute the terms in the following method \n", "\n", "\\begin{align}\n", " u_{j+1} &= u_j + \\frac{h}{2} \\left[ \n", " f(t_j, u_j) + f\\big( t_{j+1}, u_j + h f(t_j, u_j) \\big)\n", " \\right]\n", "\\end{align}\n", "\n", "explicitly. What is the order of accuracy of this method?\n", "\n", ":::" ] } ], "metadata": { "kernelspec": { "display_name": "Julia 1.11", "language": "julia", "name": "julia-1.11" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.11.6" } }, "nbformat": 4, "nbformat_minor": 5 }