{
"cells": [
{
"cell_type": "markdown",
"id": "81b1d2f0",
"metadata": {},
"source": [
"---\n",
"title: \"Euler's Method\"\n",
"subtitle: \"Lecture 3\"\n",
"date: 2026-01-28\n",
"abstract-title: Overview\n",
"abstract: | \n",
" (1) Basics of Euler's method, \n",
" (2) Examples,\n",
" (3) Error estimates\n",
"format:\n",
" html:\n",
" other-links:\n",
" - text: This notebook\n",
" href: L3.ipynb\n",
"---"
]
},
{
"cell_type": "markdown",
"id": "63cf0867",
"metadata": {},
"source": [
"::: {.callout-note}\n",
"\n",
"I encourage you to play around with the juptyer notebook for this lecture - you can copy the code with the ```this notebook``` button on the side of this page.\n",
"\n",
":::\n",
"\n",
"::: {.callout-warning}\n",
"\n",
"These notes are mainly a record of what we discussed and are not a substitute for attending the lectures and reading books! If anything is unclear/wrong, let me know and I will update the notes.\n",
"\n",
":::\n",
"\n",
"::: {.callout-tip}\n",
"\n",
"This lecture is mostly based on @Burden section 5.2\n",
"\n",
":::"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "db6fe346",
"metadata": {},
"outputs": [],
"source": [
"#| echo: false\n",
"\n",
"using Plots, LaTeXStrings, OrdinaryDiffEq"
]
},
{
"cell_type": "markdown",
"id": "5ea01014",
"metadata": {},
"source": [
"Recall that we are considering IVPs: seek $u :[0,T] \\to \\mathbb R$ such that\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",
"We will suppose that this equation is well-posed. The numerical schemes we introduce in this section will approximate the solution $u$ to $(\\text{IVP})$ on a *mesh* $\\{t_j\\}_{j=0}^n \\subset [0,T]$. The approximation at time $t_j$ will be written $u_j$ so that $u_j \\approx u(t_j)$. We will consider the error on the mesh: $\\max_j |u(t_j) - u_j |$.\n",
"\n",
"## Euler's method\n",
"\n",
"We now fix an equispaced mesh $t_j = j\\frac{T}{n}$. We will sometimes call $h := \\frac{T}n$ the *step size*. \n",
"\n",
"Replacing the derivative in $(\\text{IVP})$ with the *forward difference* \n",
"\n",
"\\begin{align}\n",
" u'(t_j) \\approx \\frac{u_{j+1} - u_j}{h} \n",
"\\end{align}\n",
"\n",
"yields Euler's method\n",
"\n",
"\\begin{align}\n",
" u_{j+1} = u_j + h f(t, u_j)\n",
" \\tag{Euler}\n",
"\\end{align}\n",
"\n",
"::: {.callout-note}\n",
"\n",
"Last time, we saw that by integrating $(\\text{IVP})$ we obtain\n",
"\n",
"\\begin{align}\n",
" u(t_{j+1}) = u(t_{j}) + \\int_{t_j}^{t_{j+1}} f\\big( s, u(s) \\big) \\mathrm{d}s.\n",
"\\end{align}\n",
"\n",
"Approximating this integral with the *rectangular rule* and replacing $u(t_j)$ with $u_j$ also yields Euler's method.\n",
"\n",
"::: \n",
"\n",
"That is, we approximate the differential equation with a *difference equation*.\n",
"\n",
"We implement Euler's method here:"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "1f847c0c",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Euler (generic function with 1 method)"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function Euler( u0, f, T, n )\n",
" h = T/n \n",
" t = 0:h:T \n",
" u = zeros(n+1)\n",
" u[1] = u0\n",
" for j = 1:n\n",
" u[j+1] = u[j] + h * f( t[j], u[j] )\n",
" end\n",
" return u\n",
"end "
]
},
{
"cell_type": "markdown",
"id": "0d920692",
"metadata": {},
"source": [
"## Examples\n",
"\n",
"We now apply Euler's method to each of the examples from Lecture 2:\n",
"\n",
"::: {#exm-1}\n",
"# Exponential growth\n",
"\n",
"We consider $u' = \\mu u$ with $u(0) = u_0 > 0$. Recall that this problem is well-posed with unique solution $u(t) = u_0 e^{\\mu t}$. We approximate this solution using Euler's method:"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "84b17ae2",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"
"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"μ = 2\n",
"f(t, u) = μ * u\n",
"u0, T, n = 1, 2, 4\n",
"\n",
"u = Euler( u0, f, T, n )\n",
"scatter( 0:T/n:T, u, \n",
" label=\"Euler (n=$n)\",\n",
" title=\"Exponential (u' = u)\")\n",
"\n",
"n=100\n",
"u2 = Euler( u0, f, T, n )\n",
"scatter!( 0:T/n:T, u2, \n",
" label=\"Euler (n=$n)\" )\n",
"\n",
"plot!(t-> u0 * exp(μ * t),\n",
" label=\"exact solution\")"
]
},
{
"cell_type": "markdown",
"id": "03a17bc0",
"metadata": {},
"source": [
"In the following, we plot the errors as a function of $n$:"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "5536e267",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"image/svg+xml": [
"\n",
"