{ "cells": [ { "cell_type": "markdown", "id": "81b1d2f0", "metadata": {}, "source": [ "---\n", "title: \"Runge-Kutta Methods\"\n", "subtitle: \"Lecture 5\"\n", "date: 2026-02-09\n", "abstract-title: Overview\n", "abstract: | \n", " (1) Recap \n", " (2) RK4\n", " (3) Adaptive RK\n", " (4) Examples \n", "format:\n", " html:\n", " other-links:\n", " - text: This notebook\n", " href: L5.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 5.4 & 5.5\n", "\n", ":::" ] }, { "cell_type": "code", "execution_count": 1, "id": "db6fe346", "metadata": {}, "outputs": [], "source": [ "#| echo: false\n", "\n", "# IF YOU ARE READING THIS, THANK YOU\n", "# FOR DOWNLOADING THE LECTURE NOTES.\n", "# THE FIRST PERSON TO LET ME KNOW,\n", "# WINS SOME CHOCOLATES OF YOUR CHOICE\n", "\n", "using Plots, LaTeXStrings, OrdinaryDiffEq" ] }, { "cell_type": "markdown", "id": "5ea01014", "metadata": {}, "source": [ "## Recap\n", "\n", "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 $f$ is continuous on $[0,T] \\times \\mathbb R$ and Lipschitz in the second argument and so the problem is well-posed and there exists a unique solution to $(\\text{IVP})$. Recall *one-step methods*: \n", "\n", "\\begin{align}\n", " u_{j+1} = u_j + h \\phi(t_j, u_j; h)\n", " \\tag{1-step}\n", "\\end{align}\n", "\n", "where $t_j = j \\frac{T}{n} = j h$ define the *mesh*. We saw last week that, if the local truncation error is $\\tau_{j+1} = O(h^p)$ as $h\\to 0$ (i.e. if the method is *consistent* with *order of accuracy $p$*) and $|\\frac{\\partial \\phi}{\\partial u}| \\leq L$ on $[0,T] \\times \\mathbb R$, then we have the error bound \n", "\n", "\\begin{align}\n", " |u(t_j) - u_j| \\leq \\frac{Ch^p}{L} ( e^{Lt_j} - 1).\n", "\\end{align}\n", "\n", "Then, we looked at particular examples of $\\phi$:\n", "\n", "***Taylor methods:*** use the expansion $u(t_{j+1}) = u(t_j) + h u'(t_j) + \\frac{h^2}{2} u''(t_j) + \\dots$ and use the fact that $u'(t) = f(t, u(t))$ to evaluate the higher derivatives:\n", "\n", "\\begin{align}\n", " \\frac{u(t_{j+1}) - u(t_j)}{h} \n", " %\n", " &= f(t_j, u(t_j)) \\nonumber\\\\\n", " %\n", " &+ \\frac{h}{2} \\left[ \\frac{\\partial f}{\\partial t}(t_j, u(t_j)) + \\frac{\\partial f}{\\partial u}(t_j, u(t_j)) f(t_j, u(t_j))\\right] + \\dots\n", "\\end{align}\n", "\n", "* Taylor method of order $1$ is just Euler's method, \n", "* Taylor method of order $2$ truncates the expansion at the next order: \n", "\n", "\\begin{align}\n", " \\phi = f + \\frac{h}{2}\\Big( \\frac{\\partial f}{\\partial t} + \\frac{\\partial f}{\\partial u} f \\Big).\n", "\\end{align}\n", "\n", "The downside of these methods is that they require higher order derivatives of $f$ to be known exactly.\n", "\n", "## Runge-Kutta Methods\n", "\n", "Last week, we looked for an order $2$ method with $\\phi = f(t + \\alpha, u + \\beta)$. That is, we expanded \n", "\n", "\\begin{align}\n", " \\kappa_{j+1}(h) := \\frac{u(t_{j+1}) - u(t_j)}{h}\n", " %\n", " - f\\big( t_j + \\alpha, u(t_j) + \\beta \\big) \\nonumber\n", "\\end{align}\n", "\n", "in $\\alpha, \\beta$ and found that, under the choice $\\alpha := \\frac{h}{2}$ and $\\beta := \\frac{h}{2} f(t_j, u_j)$, the local truncation error is $\\kappa_{j+1}(h) = O(h^2)$. This method is known as the *midpoint* method: \n", "\n", "\\begin{align} \n", " u_{j+1} = u_j + h f\\big( t_j + \\tfrac{h}{2}, u_j + \\tfrac{h}{2} f(t_j,u_j) \\big).\n", " \\tag{midpoint}\n", "\\end{align} \n", "\n", "We can also write this as a *multi-stage method*:\n", "\n", "\\begin{align}\n", " k_1 &:= h f(t_j, u_j) \\nonumber\\\\\n", " k_2 &:= h f(t_j + \\tfrac12 h, u_j + \\tfrac12 k_1) \\nonumber\\\\\n", " u_{j+1} &:= u_j + k_2 \n", " \\tag{midpoint'}\n", "\\end{align}" ] }, { "cell_type": "markdown", "id": "cc1ca527", "metadata": {}, "source": [ "::: {#def-RK}\n", "\n", "A general $s$-stage Runge-Kutta method is of the form:\n", "\n", "\\begin{align}\n", " k_1 &= h f(t_j, u_j) \\nonumber\\\\\n", " k_2 &= h f(t_j + c_1 h, u_j + a_{11} k_1) \\nonumber \\\\\n", " k_3 &= h f(t_j + c_2 h, u_j + a_{21} k_1 + a_{22} k_2) \\nonumber\\\\\n", " \\vdots& \\nonumber\\\\\n", " k_s &= h f(t_j + c_{s-1} h, u_j + a_{s-1,1} k_1 + \\dots + a_{s-1,s-1} k_{s-1}) \\nonumber\\\\\n", " %\n", " u_{j+1} &= u_{j} + b_1 k_1 + b_2 k_2 + \\dots + b_s k_s. \\nonumber\n", "\\end{align}\n", "\n", "This Runge-Kutta method is conveniently written as the *Butcher tableau*: \n", "\n", "\\begin{array}\n", "{c|cccc}\n", "0\\\\\n", "c_1 & a_{11} \\\\\n", "c_2 & a_{21} & a_{22} \\\\\n", "\\vdots & \\vdots& \\vdots & \\ddots& \\\\\n", "c_{s-1} & a_{s-1,1}& a_{s-1,2} & \\cdots & a_{s-1,s-1} \\\\\n", "\\hline\n", "& b_1 & b_2 & \\dots & b_{s-1} & b_s \n", "\\end{array}\n", "\n", ":::\n", "\n", "::: {#exr-3}\n", "\n", "Write down the Butcher tableau for *(i)* Euler's method, *(ii)* Midpoint method (also known as *improved Euler's method*), and the following $2$-stage, order $2$ methods:\n", "\n", "*(iii)*: Modified Euler\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", "*(iv)*: Heun's method\n", "\\begin{align}\n", " u_{j+1} &= u_j + \\frac{h}{4} \\left[ \n", " f(t_j, u_j) + 3 f\\big( t_{j} + \\tfrac{2}{3} h, u_j + \\tfrac{2}{3} h f(t_j, u_j) \\big)\n", " \\right]\n", "\\end{align}\n", "\n", ":::\n", "\n", "::: {#exm-22}\n", "\n", "Show that all $2$ stage, order $2$ Runge-Kutta methods have a Butcher tableau of the form\n", "\n", "\\begin{array}\n", "{c|cccc}\n", "0\\\\\n", "\\tfrac{1}{2b} & \\tfrac{1}{2b} \\\\\n", "\\hline\n", "& 1-b & b \n", "\\end{array}\n", "\n", "for some $b \\not= 0$. \n", "\n", ":::\n", "\n", "Here, we implement a general RK method:\n" ] }, { "cell_type": "code", "execution_count": 2, "id": "531cf298", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "RK (generic function with 1 method)" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function RK( u0, f, T, n, A, b, c )\n", " h = T/n \n", " t = 0:h:T \n", " u = fill(float(u0), n+1)\n", " s, = size(A)\n", " s = s+1 \n", " k = fill(float(u0), s)\n", " for j = 1:n\n", " k[1] = h * f( t[j], u[j] )\n", " for i = 1:s-1 \n", " k[i+1] = h * f( t[j] + h * c[i], u[j] + sum( A[i,ℓ] * k[ℓ] for ℓ ∈ 1:i ) )\n", " end\n", " u[j+1] = u[j] + sum( b[ℓ] * k[ℓ] for ℓ ∈ 1:s )\n", " end\n", " return u\n", "end " ] }, { "cell_type": "markdown", "id": "bf3fea6e", "metadata": {}, "source": [ "::: {#exm-RK}\n", "\n", "Here, we solve \n", "\n", "\\begin{align}\n", " u(0) &= u_0 \\nonumber\\\\\n", " u'(t) &= \\cos u(t) + \\sin t \n", "\\end{align}\n", "\n", "with different initial conditions using the ```OrdinaryDiffEq``` package: " ] }, { "cell_type": "code", "execution_count": 3, "id": "3641daf0", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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$u0\",\n", " xlabel=L\"t\", ylabel=L\"u(t)\")\n", "\n", "for u0 = vcat(0:.1:2π, [π/2,π,3π/2,2π])\n", " ivp = ODEProblem((u,p,t)->f(t,u), u0, (0.,T))\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": "366a2d65", "metadata": {}, "source": [ "We next apply *(i)* Euler, *(ii)* midpoint, *(iii)* modified Euler, and *(iv)* Heun's method and plot the errors as a function of $n$:" ] }, { "cell_type": "code", "execution_count": 4, "id": "ba24b346", "metadata": {}, "outputs": [ { "data": { "image/png": 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[1/2], [0, 1], [1/2])\n", " u3 = RK( u0, f, T, n, [1], [1/2, 1/2], [1])\n", " u4 = RK( u0, f, T, n, [2/3], [1/4, 3/4], [2/3])\n", " mesh = 0:T/n:T\n", " errs[ℓ,1] = maximum( @. abs( u1 - sol(mesh) ) )\n", " errs[ℓ,2] = maximum( @. abs( u2 - sol(mesh) ) )\n", " errs[ℓ,3] = maximum( @. abs( u3 - sol(mesh) ) )\n", " errs[ℓ,4] = maximum( @. abs( u4 - sol(mesh) ) )\n", "end\n", "\n", "plot(nn, errs[:,1:4];\n", " m=3, label=[\"Euler\" \"Midpoint\" \"Modified Euler\" \"Heun\"], \n", " xaxis=(:log10, L\"n\"), yaxis=:log10,\n", " title=\"Error\")\n", "plot!( nn, (1/2)*errs[end,1]*(nn/nn[end]).^(-1), label=L\"O(n^{-1})\", linestyle=:dash )\n", "plot!( nn, (1/2)*errs[end,4]*(nn/nn[end]).^(-2), label=L\"O(n^{-2})\", linestyle=:dash )" ] }, { "cell_type": "markdown", "id": "84c09b2b", "metadata": {}, "source": [ ":::" ] }, { "cell_type": "markdown", "id": "08b0ca85", "metadata": {}, "source": [ "Section 5.4 of @Burden.\n", "\n", "The most common RK method is $4$-stage, order $4$ method given by the followng Butcher tableau:\n", "\n", "\\begin{align}\\tag{RK4}\n", "\\begin{array}\n", "{c|cccc}\n", "0\\\\\n", "\\frac12 & \\frac12 \\\\\n", "\\frac12 & 0 & \\frac12 \\\\\n", "1 & 0 & 0 & 1 \\\\\n", "\\hline\n", "& \\frac16 & \\frac13 & \\frac13 & \\frac16 \n", "\\end{array}\n", "\\end{align}\n", "\n", "::: {#exm-RK2}\n", "\n", "We apply $(\\text{RK4})$ to @exm-RK:" ] }, { "cell_type": "code", "execution_count": 5, "id": "ad7e5276", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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"end\n", "\n", "plot(nn, errs;\n", " m=4, label=[\"Euler\" \"Midpoint\" \"Modified Euler\" \"Heun\" \"RK4\"], \n", " xaxis=(:log10, L\"n\"), yaxis=:log10, ylims=(1e-11,1e2),\n", " title=\"Error\")\n", "plot!( nn, (1/2)*errs[end,1]*(nn/nn[end]).^(-1), label=L\"O(n^{-1})\", linestyle=:dash )\n", "plot!( nn, (1/2)*errs[end,4]*(nn/nn[end]).^(-2), label=L\"O(n^{-2})\", linestyle=:dash )\n", "plot!( nn, (1/100)*errs[end,5]*(nn/nn[end]).^(-4), label=L\"O(n^{-4})\", linestyle=:dash )" ] }, { "cell_type": "markdown", "id": "ae6dc453", "metadata": {}, "source": [ ":::\n", "\n", "We want to compare the error made with the computational cost involved (rather than $n$). \n", "\n", "Euler:\n", "\n", "\\begin{align}\n", " u_{j+1} = u_j + h f( t_j, u_j)\n", "\\end{align}\n", "\n", "General 2 stage RK: \n", "\n", "\\begin{align}\n", " u_{j+1} = u_j &+ b_1 h f(t_j, u_j) \\nonumber\\\\\n", " &+ b_2 h f\\big( t_j + c_1 h, u_j + a_{11} h f(t_j, u_j) \\big)\n", "\\end{align}\n", "\n", "::: {#exr-1}\n", "\n", "How many function evaluations are needed to implement these methods? What about a general $s$-stage RK method?\n", "\n", ":::\n", "\n", "::: {#exm-RK2}\n", "\n", "We return to @exm-RK and plot the errors against the function evaluations:" ] }, { "cell_type": "code", "execution_count": 6, "id": "36cef2d3", "metadata": {}, "outputs": [ { "data": { "image/png": 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(1/2)*errs[end,1]*(nn/nn[end]).^(-1), label=L\"O(n^{-1})\", linestyle=:dash )\n", "plot!( 2nn, (1/2)*errs[end,4]*(nn/nn[end]).^(-2), label=L\"O(n^{-2})\", linestyle=:dash )\n", "plot!( 4nn, (1/100)*errs[end,5]*(nn/nn[end]).^(-4), label=L\"O(n^{-4})\", linestyle=:dash )" ] }, { "cell_type": "markdown", "id": "45536451", "metadata": {}, "source": [ ":::\n", "\n", "A general $s$-stage RK method requires $s$ function evaluations. \n", "\n", "* We have seen that Euler ($1$-stage RK method) has order $1$, \n", "* We have seen many (we have written them all down!) $2$-stage, order $2$ methods, \n", "* RK4 is a $4$-stage, order $4$ method (there are many others), \n", "* **However**, if $s\\geq 5$, the best possible order of accuracy is $p < s$.\n", "\n", "(For $5 \\leq s \\leq 7$ the maximal order of accuracy is $s-1$ and, for $8 \\leq s \\leq 9$ the maximal order of accuracy is $s-2$ and, for $s \\geq 10$, the maximal order of accuracy is $s-3$.) " ] }, { "cell_type": "markdown", "id": "a46cef2f", "metadata": {}, "source": [ "## Adaptive RK methods\n", "\n", "Here, we look at example 6.1.8 from @FNC:\n", "\n", "::: {#exm-parachute}\n", "\n", "A model for the velocity $v(t)$ of a skydiver at time $t$ is given by\n", "\n", "\\begin{align}\n", " v(0) &= 0 \\nonumber\\\\\n", " \\dot{v}(t) &= -g + \\frac{k(t)}{m} v(t)^2\n", "\\end{align}\n", "\n", "where $g \\approx 9.81 \\text{m/s}^2$ is the acceleration due to gravity, $m$ is the mass of the skydiver, and $k(t)$ models the effects of air-resistance. A simple model for $k$ is given as a step function: \n", "\n", "\\begin{align}\n", " k(t) &= \\begin{cases}\n", " k_1 & \\text{if }t \\leq t_1 \\nonumber\\\\\n", " k_2 & \\text{if }t > t_1\n", " \\end{cases}\n", "\\end{align}\n", "\n", "where $k_2 > k_1$ and $t_1$ is the time at which the parachute is deployed. \n", "\n", "What do you expect the solution to look like?\n", "\n", "Here, we implement the RK4 method and the scheme included in ```OrdinaryDiffEq```:" ] }, { "cell_type": "code", "execution_count": 13, "id": "aacb03a4", "metadata": {}, "outputs": [ { "data": { "image/png": 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"image/svg+xml": [ "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "text/html": [ "" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t1 = 2π\n", "k(t) = t<=t1 ? 1 : 50\n", "f(t,v) = -9.81 + (1/80) * k(t) * v^2\n", "v0, T, n = 0., 10., 100\n", "\n", "ivp = ODEProblem((v,p,t)->f(t,v), v0, (0., T))\n", "sol = solve(ivp, Tsit5())\n", "N = length(sol.t)\n", "\n", "v = RK( v0, f, T, n, A, b, c)\n", "\n", "plot(sol,\n", " title=\"Velocity of a skydiver\", \n", " label=\"Tsit5 (n=$N)\", xlabel=L\"t\", ylabel=L\"v(t)\", \n", " ylims=(-28,0))\n", "plot!(0:T/n:T, v, label=\"RK4 (n=$n)\")" ] }, { "cell_type": "code", "execution_count": 14, "id": "3d7276c1", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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"ebb775c7", "metadata": {}, "source": [ "Section 5.5 of @Burden\n", "\n", "Here, we implement a adaptive Runge-Kutta algorithm:" ] }, { "cell_type": "code", "execution_count": 11, "id": "cf3d2bd1", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "ARK (generic function with 1 method)" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function ARK( u0, f, T; A=[1/2 0 0 ; 0 3/4 0 ; 2/9 1/3 4/9], b=[2/9 1/3 4/9 0; 7/24 1/4 1/3 1/8], c=[1/2 3/4 1], tol=1e-5, p=2)\n", " \n", " t = [0.]\n", " u = [float(u0)]\n", " s, = size(A)\n", " s = s+1 \n", " k = fill(float(u0), s)\n", " i = 1\n", " h = 1\n", "\n", " k = fill(float(u0), s)\n", " \n", " # Time stepping.\n", " while t[i] < T\n", " if h < 1e-15\n", " @warn \"Step size is too small, t=$(t[i])\"\n", " break \n", " end\n", "\n", " k[1] = h * f( t[i], u[i] )\n", " for j = 1:s-1 \n", " k[j+1] = h * f( t[i] + h * c[j], u[i] + sum( A[j,ℓ] * k[ℓ] for ℓ ∈ 1:j ) )\n", " end\n", " next_u_1 = u[i] + sum( b[1,ℓ] * k[ℓ] for ℓ ∈ 1:(s-1) )\n", " next_u_2 = u[i] + sum( b[2,ℓ] * k[ℓ] for ℓ ∈ 1:s )\n", " E = abs(next_u_1 - next_u_2)\n", "\n", " if E < tol\n", " push!(t, t[i] + h)\n", " push!(u, next_u_2)\n", " i += 1\n", " end\n", "\n", " # step size\n", " q = 0.85 * (tol/E)^(1/(p+1)) \n", " q = min(q, 2) \n", " h = min(q*h, T-t[i]) \n", " end\n", " return t, u\n", "end" ] }, { "cell_type": "markdown", "id": "d9b769e1", "metadata": {}, "source": [ "::: {#exm-parachute-2}\n", "\n", "We use this method to numerically solve @exm-parachute:" ] }, { "cell_type": "code", "execution_count": 12, "id": "00ca922d", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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= length(t) \n", "\n", "plot(sol,\n", " title=\"Velocity of a skydiver\", \n", " label=\"Tsit5 (n=$N)\", xlabel=L\"t\", ylabel=L\"v(t)\", \n", " ylims=(-28,0))\n", "plot!(t, v, m=3, label=\"ARK (n=$n)\")" ] }, { "cell_type": "markdown", "id": "b8ee6891", "metadata": {}, "source": [ ":::" ] }, { "cell_type": "markdown", "id": "b94ee96d", "metadata": {}, "source": [ ":::{.callout-tip}\n", "# TO-DO\n", "\n", "* Assignment 2: Due Wednesday 11:59 PM,\n", "* Read: @Burden sections 5.1 - 5.5,\n", "* (Sign-up to office hours if you would like)\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 }