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"source": "# Simple gravity pendulum\n\nSimple gravity pendulum:\n$$\n\\frac{d^2\\theta}{dt^2} = -\\frac{g}{l}\\sin\\theta.\n$$\n\nInitial condition for $-1 < y_{\\mathrm{max}} < 1$\n$$\n\\theta(0) = 0, \\quad\n\\dot\\theta(0) = \\sqrt{\\frac{g}{l}}\\;2y_{\\mathrm{max}}\n$$\n\nExact solution:\n$$\n\\theta(t) = 2\\arcsin\\left(\n y_{max}\\mathrm{sn}\\left(\\sqrt{\\frac{g}{l}}\\;t\\;\\Bigg|\\;k=y_{\\mathrm{max}}\\right)\n\\right)\n$$"
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"source": "<h1>Table of Contents<span class=\"tocSkip\"></span></h1>\n<div class=\"toc\"><ul class=\"toc-item\"><li><span><a href=\"#ODEProblem\" data-toc-modified-id=\"ODEProblem-1\"><span class=\"toc-item-num\">1 </span>ODEProblem</a></span><ul class=\"toc-item\"><li><span><a href=\"#ODEProblem:-in-place-version\" data-toc-modified-id=\"ODEProblem:-in-place-version-1.1\"><span class=\"toc-item-num\">1.1 </span>ODEProblem: in-place version</a></span></li><li><span><a href=\"#ODEProblem:-SVector-version\" data-toc-modified-id=\"ODEProblem:-SVector-version-1.2\"><span class=\"toc-item-num\">1.2 </span>ODEProblem: SVector version</a></span></li></ul></li><li><span><a href=\"#SecondOrderODEProblem\" data-toc-modified-id=\"SecondOrderODEProblem-2\"><span class=\"toc-item-num\">2 </span>SecondOrderODEProblem</a></span></li><li><span><a href=\"#DynamicalODEProblem\" data-toc-modified-id=\"DynamicalODEProblem-3\"><span class=\"toc-item-num\">3 </span>DynamicalODEProblem</a></span></li><li><span><a href=\"#HamiltonianProblem\" data-toc-modified-id=\"HamiltonianProblem-4\"><span class=\"toc-item-num\">4 </span>HamiltonianProblem</a></span></li><li><span><a href=\"#Simple-Runge-Kutta-Order-4\" data-toc-modified-id=\"Simple-Runge-Kutta-Order-4-5\"><span class=\"toc-item-num\">5 </span>Simple Runge-Kutta Order 4</a></span></li><li><span><a href=\"#Benchmark\" data-toc-modified-id=\"Benchmark-6\"><span class=\"toc-item-num\">6 </span>Benchmark</a></span></li></ul></div>"
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"source": "@show VERSION\n\nsecond(a) = a[begin+1]\n\n@time using Printf\n@time using DifferentialEquations\n@time using StaticArrays\n@time using Parameters\n@time using Elliptic\n\n@time using Plots\n@time pyplot(fmt=:svg)\n\n@time using Unitful\nBase.zero(::Type{Quantity{T}}) where T = zero(T)\nconst m = u\"m\"\nconst s = u\"s\"\nval(x) = x\nval(x::Unitful.AbstractQuantity) = x.val\n\n@time using PhysicalConstants\ng = PhysicalConstants.CODATA2018.StandardAccelerationOfGravitation",
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"text": "VERSION = v\"1.7.0-DEV.1129\"\n 0.001262 seconds (1.61 k allocations: 117.172 KiB, 135.22% compilation time)\n 8.646942 seconds (21.28 M allocations: 1.542 GiB, 4.93% gc time)\n 0.021959 seconds (33.37 k allocations: 1.902 MiB, 97.53% compilation time)\n 0.000396 seconds (251 allocations: 16.391 KiB)\n 0.003836 seconds (3.21 k allocations: 282.844 KiB, 28.24% compilation time)\n 3.418940 seconds (6.87 M allocations: 508.058 MiB, 7.96% gc time)\n 4.658772 seconds (12.27 M allocations: 735.629 MiB, 3.57% gc time, 0.35% compilation time)\n 0.022045 seconds (33.37 k allocations: 1.902 MiB, 97.57% compilation time)\n 0.312106 seconds (459.72 k allocations: 30.415 MiB)\n",
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"text": "WARNING: Wrapping `Vararg` directly in UnionAll is deprecated (wrap the tuple instead).\n",
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"text/plain": "Standard acceleration of gravitation (g_n)\nValue = 9.80665 m s^-2\nStandard uncertainty = (exact)\nRelative standard uncertainty = (exact)\nReference = CODATA 2018"
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"source": "# parameters with dimensions\ng = PhysicalConstants.CODATA2018.StandardAccelerationOfGravitation # = 9.80665 m/s²\nl = 1.0m\nθ0 = 0.0\nymax = 0.9999 # this setting is very stiff!\ndθ0 = √(g/l)*2ymax\nt0 = 0.0s\nt1 = 30.0s\n\n# dimensionless parameters\np = val.((g, l)) \ntspan = val.((t0, t1))\nv0 = val.([dθ0])\nu0 = val.([θ0])\nvu0 = val.([dθ0, θ0])\n\n(; p, ymax, vu0)",
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"text/plain": "(p = (9.80665, 1.0), ymax = 0.9999, vu0 = [6.262487929909805, 0.0])"
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"source": "# exact solution for θ0 = 0, dθ(0)/dt = √(g/l)*2y_max\nsn(u, k) = Jacobi.sn(u, k^2)\nθ_exact_sol(p, t, ymax) = ((g, l) = p; 2asin(ymax*sn(√(g/l)*t, ymax)))\n\nt = range(tspan...; length=1001)\nplot(t, θ_exact_sol.(Ref(p), t, ymax); label=\"exact solution\", ylim=(-4, 5.5))\nplot!(; size=(400, 250))",
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"text": "┌ Warning: `vendor()` is deprecated, use `BLAS.get_config()` and inspect the output instead\n│ caller = npyinitialize() at numpy.jl:67\n└ @ PyCall C:\\Users\\genkuroki\\.julia\\packages\\PyCall\\BD546\\src\\numpy.jl:67\n",
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"source": "# total energy\nE(v, u, p, t) = ((g, l) = p; v[1]^2/2 - (g/l)*(cos(u[1]) - 1))",
"execution_count": 4,
"outputs": [
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"data": {
"text/plain": "E (generic function with 1 method)"
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"source": "# plot function\nfunction plot_pendulum(sol, ymax; title=\"solution: θ(t)\")\n @unpack tspan, p = sol.prob\n t = range(tspan..., length=501)\n dθ = (t -> sol(t)[1]).(t)\n θ = (t -> sol(t)[2]).(t)\n θ_exact = θ_exact_sol.(Ref(p), t, ymax)\n \n P = plot(t, [θ θ_exact]; label=[\"numerical\" \"exact\"], ls=:auto, ylim=(-4, 6.5))\n plot!(xtick=0:2:30, ytick=-10:10)\n title!(title; titlefontsize=12)\n \n v0, u0 = first.((dθ, θ))\n E_exact = fill(E(v0, u0, p, 0.0), length(t))\n E_numerical = E.(dθ, θ, Ref(p), t)\n Q = plot(t, E_numerical - E_exact; label=\"\")\n title!(\"total energy error\"; titlefontsize=12)\n plot!(xtick=0:2:30)\n \n plot(P, Q; size=(800, 250), layout=(1, 2))\nend",
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"text/plain": "plot_pendulum (generic function with 1 method)"
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"source": "## ODEProblem"
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"cell_type": "markdown",
"source": "### ODEProblem: in-place version"
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"source": "# u = [dθ/dt, θ]\n# du = [d²θ/dt², dθ/dt]\nfunction f!(du, u, p, t)\n g, l = p\n du[1] = -(g/l)*sin(u[2])\n du[2] = u[1]\nend\n\node_prob = ODEProblem(f!, vu0, tspan, p)\n@time sol = solve(ode_prob)\n@time sol = solve(ode_prob)\n@time sol = solve(ode_prob)\n@show length(sol.t)\n\nplot_pendulum(sol, ymax)",
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"text": " 24.767610 seconds (57.54 M allocations: 3.365 GiB, 3.73% gc time)\n 0.000175 seconds (1.16 k allocations: 122.750 KiB)\n 0.000151 seconds (1.16 k allocations: 122.750 KiB)\nlength(sol.t) = 113\n",
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"source": "# u = [dθ/dt, θ]\n# du = [d²θ/dt², dθ/dt]\nfunction f!(du, u, p, t)\n g, l = p\n du[1] = -(g/l)*sin(u[2])\n du[2] = u[1]\nend\n\node_prob = ODEProblem(f!, vu0, tspan, p)\n@time sol = solve(ode_prob, RKO65(); dt=0.05)\n@time sol = solve(ode_prob, RKO65(); dt=0.05)\n@time sol = solve(ode_prob, RKO65(); dt=0.05)\n@show length(sol.t)\n\nplot_pendulum(sol, ymax)",
"execution_count": 7,
"outputs": [
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"text": " 2.895777 seconds (6.72 M allocations: 386.049 MiB, 3.10% gc time)\n 0.000254 seconds (4.84 k allocations: 487.719 KiB)\n 0.000253 seconds (4.84 k allocations: 487.719 KiB)\nlength(sol.t) = 601\n",
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"source": "### ODEProblem: SVector version"
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"source": "# u = [dθ/dt, θ]\n# du = [d²θ/dt², dθ/dt]\nfunction f(u, p, t)\n g, l = p\n du = SVector(\n -(g/l)*sin(u[2]),\n u[1]\n )\nend\n\node_prob = ODEProblem(f, SVector{2}(vu0), tspan, p)\n@time sol = solve(ode_prob)\n@time sol = solve(ode_prob)\n@time sol = solve(ode_prob)\n@show length(sol.t)\n\nplot_pendulum(sol, ymax)",
"execution_count": 8,
"outputs": [
{
"output_type": "stream",
"text": " 3.441609 seconds (10.25 M allocations: 628.632 MiB, 4.34% gc time)\n 0.000074 seconds (187 allocations: 40.328 KiB)\n 0.000068 seconds (187 allocations: 40.328 KiB)\nlength(sol.t) = 114\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 8,
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"source": "# u = [dθ/dt, θ]\n# du = [d²θ/dt², dθ/dt]\nfunction f(u, p, t)\n g, l = p\n du = SVector(\n -(g/l)*sin(u[2]),\n u[1]\n )\nend\n\node_prob = ODEProblem(f, SVector{2}(vu0), tspan, p)\n@time sol = solve(ode_prob, RKO65(); dt=0.05)\n@time sol = solve(ode_prob, RKO65(); dt=0.05)\n@time sol = solve(ode_prob, RKO65(); dt=0.05)\n@show length(sol.t)\n\nplot_pendulum(sol, ymax)",
"execution_count": 9,
"outputs": [
{
"output_type": "stream",
"text": " 0.651616 seconds (2.57 M allocations: 153.325 MiB, 5.61% gc time)\n 0.000243 seconds (622 allocations: 124.797 KiB)\n 0.000112 seconds (622 allocations: 124.797 KiB)\nlength(sol.t) = 601\n",
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"source": "## SecondOrderODEProblem"
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"source": "# u = [θ], v = [dθ/dt]\n# du = [dθ/dt], dv = [d²θ/dt²]\nf2!(dv, v, u, p, t) = ((g, l) = p; dv[1] = -(g/l)*sin(u[1]))\n\nsoode_prob = SecondOrderODEProblem(f2!, v0, u0, tspan, p)\n@time sol = solve(soode_prob)\n@time sol = solve(soode_prob)\n@time sol = solve(soode_prob)\n@show length(sol.t)\n\nplot_pendulum(sol, ymax)",
"execution_count": 10,
"outputs": [
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"text": " 5.784741 seconds (26.73 M allocations: 1.312 GiB, 6.42% gc time)\n 0.000185 seconds (2.01 k allocations: 210.750 KiB)\n 0.000179 seconds (2.01 k allocations: 210.750 KiB)\nlength(sol.t) = 113\n",
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"source": "# u = [θ], v = [dθ/dt]\n# du = [dθ/dt], dv = [d²θ/dt²]\nf2!(dv, v, u, p, t) = ((g, l) = p; dv[1] = -(g/l)*sin(u[1]))\n\nsoode_prob = SecondOrderODEProblem(f2!, v0, u0, tspan, p)\n@time sol = solve(soode_prob, Yoshida6(); dt=0.1)\n@time sol = solve(soode_prob, Yoshida6(); dt=0.1)\n@time sol = solve(soode_prob, Yoshida6(); dt=0.1)\n@show length(sol.t)\n\nplot_pendulum(sol, ymax)",
"execution_count": 11,
"outputs": [
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"text": " 1.609789 seconds (6.28 M allocations: 325.435 MiB, 4.86% gc time)\n 0.000181 seconds (2.14 k allocations: 215.203 KiB)\n 0.000211 seconds (2.14 k allocations: 215.203 KiB)\nlength(sol.t) = 301\n",
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"source": "## DynamicalODEProblem"
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"source": "# u = [θ], v = [dθ/dt]\n# du = [dθ/dt], dv = [d²θ/dt²]\nf1!(du, v, u, p, t) = @. du = v\nf2!(dv, v, u, p, t) = ((g, l) = p; dv[1] = -(g/l)*sin(u[1]))\n\ndynode_prob = DynamicalODEProblem(f2!, f1!, v0, u0, tspan, p)\n@time sol = solve(dynode_prob)\n@time sol = solve(dynode_prob)\n@time sol = solve(dynode_prob)\n@show length(sol.t)\n\nplot_pendulum(sol, ymax)",
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"text": " 3.786276 seconds (7.95 M allocations: 421.076 MiB, 11.20% gc time)\n 0.000202 seconds (2.01 k allocations: 210.750 KiB)\n 0.000185 seconds (2.01 k allocations: 210.750 KiB)\nlength(sol.t) = 113\n",
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"source": "# u = [θ], v = [dθ/dt]\n# du = [dθ/dt], dv = [d²θ/dt²]\nf1!(du, v, u, p, t) = @. du = v\nf2!(dv, v, u, p, t) = ((g, l) = p; dv[1] = -(g/l)*sin(u[1]))\n\ndynode_prob = DynamicalODEProblem(f2!, f1!, v0, u0, tspan, p)\n@time sol = solve(dynode_prob, Yoshida6(); dt=0.1)\n@time sol = solve(dynode_prob, Yoshida6(); dt=0.1)\n@time sol = solve(dynode_prob, Yoshida6(); dt=0.1)\n@show length(sol.t)\n\nplot_pendulum(sol, ymax)",
"execution_count": 13,
"outputs": [
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"text": " 1.197207 seconds (2.85 M allocations: 153.838 MiB, 1.93% gc time)\n 0.000305 seconds (2.14 k allocations: 215.203 KiB)\n 0.000161 seconds (2.14 k allocations: 215.203 KiB)\nlength(sol.t) = 301\n",
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"source": "## HamiltonianProblem"
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"source": "# u = [θ], v = [dθ/dt]\nH(v, u, p, t) = ((g, l) = p; v[1]^2/2 - (g/l)*(cos(u[1]) + 1))\n\nhamil_prob = HamiltonianProblem(H, v0, u0, tspan, p)\n@time sol = solve(hamil_prob)\n@time sol = solve(hamil_prob)\n@time sol = solve(hamil_prob)\n@show length(sol.t)\n\nplot_pendulum(sol, ymax)",
"execution_count": 14,
"outputs": [
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"text": " 3.876122 seconds (9.92 M allocations: 534.090 MiB, 3.83% gc time)\n 0.000228 seconds (2.01 k allocations: 211.141 KiB)\n 0.000214 seconds (2.01 k allocations: 211.141 KiB)\nlength(sol.t) = 113\n",
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"source": "# u = [θ], v = [dθ/dt]\nH(v, u, p, t) = ((g, l) = p; v[1]^2/2 - (g/l)*(cos(u[1]) + 1))\n\nhamil_prob = HamiltonianProblem(H, v0, u0, tspan, p)\n@time sol = solve(hamil_prob, Yoshida6(); dt=0.1)\n@time sol = solve(hamil_prob, Yoshida6(); dt=0.1)\n@time sol = solve(hamil_prob, Yoshida6(); dt=0.1)\n@show length(sol.t)\n\nplot_pendulum(sol, ymax)",
"execution_count": 15,
"outputs": [
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"text": " 1.235402 seconds (2.95 M allocations: 159.639 MiB, 2.50% gc time)\n 0.000278 seconds (2.14 k allocations: 215.516 KiB)\n 0.000295 seconds (2.14 k allocations: 215.516 KiB)\nlength(sol.t) = 301\n",
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"cell_type": "markdown",
"source": "## Simple Runge-Kutta Order 4"
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"source": "function f!(du, u, p, t)\n g, l = p\n du[1] = -(g/l)*sin(u[2])\n du[2] = u[1]\nend\n\np = (g, l) = (9.80665, 1.0)\nymax = 0.9999\nv0 = [√(g/l)*2ymax]\nu0 = [0.0]\ntspan = (0.0, 30.0)",
"execution_count": 16,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 16,
"data": {
"text/plain": "(0.0, 30.0)"
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"source": "function my_simple_RK4(f!, u0, tspan, p; dt=0.1)\n t = range(tspan...; step=dt)\n n = length(t)\n u = similar(typeof(u0)[], n)\n u[1] = u0\n du1, du2, du3, du4 = similar(u0), similar(u0), similar(u0), similar(u0)\n dt_half = dt/2\n for k in 2:n\n u_prev, t_prev = u[k-1], t[k-1]\n f!(du1, u_prev , p, t_prev )\n f!(du2, u_prev + du1*dt_half, p, t_prev + dt_half)\n f!(du3, u_prev + du2*dt_half, p, t_prev + dt_half)\n f!(du4, u_prev + du3*dt , p, t_prev + dt )\n u_next = @. u_prev + (du1 + 2du2 + 2du3 + du4)*dt/6\n u[k] = u_next\n end\n (; t, u)\nend",
"execution_count": 17,
"outputs": [
{
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"execution_count": 17,
"data": {
"text/plain": "my_simple_RK4 (generic function with 1 method)"
},
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]
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"source": "using SimpleDiffEq\n\ndt = 0.1\nsol = solve(ODEProblem(f!, vu0, tspan, p), SimpleRK4(); dt)\nmy_sol = my_simple_RK4(f!, vu0, tspan, p; dt)\n\n@show sol.t == my_sol.t\n@show sol.u ≈ my_sol.u\n\nplot_pendulum(sol, ymax; title=\"simple Ringe-Kutta order 4 (dt = $dt)\")",
"execution_count": 18,
"outputs": [
{
"output_type": "stream",
"text": "sol.t == my_sol.t = true\nsol.u ≈ my_sol.u = true\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 18,
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"metadata": {
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"source": "using SimpleDiffEq\n\ndt = 0.05\nsol = solve(ODEProblem(f!, vu0, tspan, p), SimpleRK4(); dt)\nmy_sol = my_simple_RK4(f!, vu0, tspan, p; dt)\n\n@show sol.t == my_sol.t\n@show sol.u ≈ my_sol.u\n\nplot_pendulum(sol, ymax; title=\"simple Ringe-Kutta order 4 (dt = $dt)\")",
"execution_count": 19,
"outputs": [
{
"output_type": "stream",
"text": "sol.t == my_sol.t = true\nsol.u ≈ my_sol.u = true\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 19,
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"source": "using SimpleDiffEq\n\ndt = 0.1\nsol_simpleRK4 = solve(ODEProblem(f!, vu0, tspan, p), SimpleRK4(); dt)\nsol_RK4 = solve(ODEProblem(f!, vu0, tspan, p), RK4(); dtmax=1.1dt)\n\n@show length(sol_simpleRK4.t)\n@show length(sol_RK4.t)\n\nt = range(tspan..., length=1001)\ndθ_simpleRK4 = (t -> sol_simpleRK4(t)[1]).(t)\nθ_simpleRK4 = (t -> sol_simpleRK4(t)[2]).(t)\ndθ_RK4 = (t -> sol_RK4(t)[1]).(t)\nθ_RK4 = (t -> sol_RK4(t)[2]).(t)\nθ_exact = θ_exact_sol.(Ref(p), t, ymax)\n\nP = plot(t, [θ_simpleRK4 θ_RK4 θ_exact];\n label=[\"SimpleRK4\" \"RK4\" \"exact\"], ls=[:solid :dash :dashdot], ylim=(-3.5, 7))\nplot!(xtick=0:2:30, ytick=-10:10)\ntitle!(\"Simple and adaptive stepping order-4 Runge-Kutta's (dt = $dt)\"; titlefontsize=8)\n\nE_exact = fill(E(v0, u0, p, 0.0), length(t))\nE_simpleRK4 = E.(dθ_simpleRK4, θ_simpleRK4, Ref(p), t)\nE_RK4 = E.(dθ_RK4, θ_RK4, Ref(p), t)\n\nQ1 = plot(t, E_simpleRK4 - E_exact; label=\"\") \ntitle!(\"total energy error of SimpleRK4\"; titlefontsize=8)\nplot!(xtick=0:2:30)\nplot!(ylim=(-0.05, 0.005))\n\nQ2 = plot(t, E_RK4 - E_exact; label=\"\") \ntitle!(\"total energy error of RK4\"; titlefontsize=8)\nplot!(xtick=0:2:30)\nplot!(ylim=(-0.05, 0.005))\n\nplot(P, Q1, Q2; size=(800, 250), layout=@layout[a [b; c]], tickfontsize=7)",
"execution_count": 20,
"outputs": [
{
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"text": "length(sol_simpleRK4.t) = 301\nlength(sol_RK4.t) = 299\n",
"name": "stdout"
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"source": "using SimpleDiffEq\n\ndt = 0.05\nsol_simpleRK4 = solve(ODEProblem(f!, vu0, tspan, p), SimpleRK4(); dt)\nsol_RK4 = solve(ODEProblem(f!, vu0, tspan, p), RK4(); dtmax=1.01dt)\n\n@show length(sol_simpleRK4.t)\n@show length(sol_RK4.t)\n\nt = range(tspan..., length=1001)\ndθ_simpleRK4 = (t -> sol_simpleRK4(t)[1]).(t)\nθ_simpleRK4 = (t -> sol_simpleRK4(t)[2]).(t)\ndθ_RK4 = (t -> sol_RK4(t)[1]).(t)\nθ_RK4 = (t -> sol_RK4(t)[2]).(t)\nθ_exact = θ_exact_sol.(Ref(p), t, ymax)\n\nP = plot(t, [θ_simpleRK4 θ_RK4 θ_exact];\n label=[\"SimpleRK4\" \"RK4\" \"exact\"], ls=[:solid :dash :dashdot], ylim=(-3.5, 7))\nplot!(xtick=0:2:30, ytick=-10:10)\ntitle!(\"Simple and adaptive stepping order-4 Runge-Kutta's (dt = $dt)\"; titlefontsize=8)\n\nE_exact = fill(E(v0, u0, p, 0.0), length(t))\nE_simpleRK4 = E.(dθ_simpleRK4, θ_simpleRK4, Ref(p), t)\nE_RK4 = E.(dθ_RK4, θ_RK4, Ref(p), t)\n\nQ1 = plot(t, E_simpleRK4 - E_exact; label=\"\") \ntitle!(\"total energy error of SimpleRK4\"; titlefontsize=8)\nplot!(xtick=0:2:30)\nplot!(ylim=(-0.001, 0.0001))\n\nQ2 = plot(t, E_RK4 - E_exact; label=\"\") \ntitle!(\"total energy error of RK4\"; titlefontsize=8)\nplot!(xtick=0:2:30)\nplot!(ylim=(-0.001, 0.0001))\n\nplot(P, Q1, Q2; size=(800, 250), layout=@layout[a [b; c]], tickfontsize=7)",
"execution_count": 21,
"outputs": [
{
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"text": "length(sol_simpleRK4.t) = 601\nlength(sol_RK4.t) = 600\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 21,
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\r\nL 423.079297 34.653969 \r\nL 423.320206 34.653898 \r\nL 423.561114 35.10404 \r\nL 423.802023 33.752858 \r\nL 424.042931 35.103835 \r\nL 424.28384 34.653483 \r\nL 424.524749 34.653502 \r\nL 424.765657 35.103775 \r\nL 425.006566 33.752997 \r\nL 425.247474 35.103817 \r\nL 425.488383 34.653579 \r\nL 425.729292 34.653607 \r\nL 425.9702 35.103899 \r\nL 426.211109 33.753137 \r\nL 426.452017 35.103956 \r\nL 426.692926 34.653722 \r\nL 426.933835 34.653751 \r\nL 427.174743 35.104056 \r\nL 427.415652 33.753279 \r\nL 427.65656 35.104156 \r\nL 427.897469 34.653958 \r\nL 428.138378 34.654007 \r\nL 428.379286 35.104563 \r\nL 428.620195 33.753424 \r\nL 428.861103 35.105148 \r\nL 429.102012 34.655176 \r\nL 429.342921 34.655394 \r\nL 429.583829 35.108126 \r\nL 429.824738 33.753591 \r\nL 430.065646 35.112356 \r\nL 430.306555 34.663695 \r\nL 430.547464 34.665106 \r\nL 430.788372 35.13347 \r\nL 431.029281 33.753905 \r\nL 431.270189 35.162637 \r\nL 431.511098 34.722012 \r\nL 431.752007 34.731428 \r\nL 431.992915 35.305249 \r\nL 432.233824 33.755182 \r\nL 432.474732 35.499387 \r\nL 432.715641 35.109142 \r\nL 432.95655 35.170947 \r\nL 433.197458 36.436254 \r\nL 433.438367 33.762617 \r\nL 433.679275 37.698037 \r\nL 433.920184 37.618771 \r\nL 434.161093 38.015177 \r\nL 434.402001 43.698191 \r\nL 434.64291 33.80777 \r\nL 434.883818 51.648551 \r\nL 435.365636 55.785534 \r\nL 435.606544 88.355484 \r\nL 435.847453 34.060242 \r\nL 436.088361 135.232639 \r\nL 436.570179 158.518508 \r\nL 436.600528 181 \r\nM 436.935587 181 \r\nL 437.051996 35.163198 \r\nL 437.117379 181 \r\nM 438.231722 181 \r\nL 438.256539 37.519074 \r\nL 438.272243 181 \r\nM 439.452788 181 \r\nL 439.461082 35.646423 \r\nL 439.467628 181 \r\nM 440.659983 181 \r\nL 440.665625 33.212453 \r\nL 440.671633 181 \r\nM 441.861771 181 \r\nL 441.870168 40.065308 \r\nL 441.881958 181 \r\nM 443.048477 181 \r\nL 443.074711 39.740413 \r\nL 443.118709 181 \r\nM 444.154801 181 \r\nL 444.279254 37.7061 \r\nL 444.506701 181 \r\nM 444.542693 181 \r\nL 444.761071 98.802602 \r\nL 445.242888 86.760047 \r\nL 445.483797 37.039304 \r\nL 445.724705 63.738951 \r\nL 445.965614 47.833753 \r\nL 446.206522 46.661934 \r\nL 446.447431 46.052308 \r\nL 446.68834 36.904127 \r\nL 446.929248 42.278556 \r\nL 447.170157 39.361225 \r\nL 447.411065 39.174581 \r\nL 447.651974 39.453648 \r\nL 447.892883 36.881202 \r\nL 448.133791 38.863726 \r\nL 448.3747 38.028566 \r\nL 448.615608 37.99982 \r\nL 448.856517 38.427803 \r\nL 449.097426 36.877668 \r\nL 449.338334 38.338001 \r\nL 449.579243 37.82492 \r\nL 449.820151 37.820622 \r\nL 450.06106 38.272464 \r\nL 450.301969 36.87724 \r\nL 450.542877 38.259238 \r\nL 450.783786 37.794774 \r\nL 451.024694 37.794179 \r\nL 451.265603 38.249847 \r\nL 451.506512 36.877295 \r\nL 451.74742 38.248068 \r\nL 451.988329 37.790673 \r\nL 452.229237 37.790621 \r\nL 452.470146 38.246926 \r\nL 452.711055 36.877425 \r\nL 452.951963 38.246776 \r\nL 453.192872 37.790314 \r\nL 453.43378 37.790336 \r\nL 453.674689 38.246752 \r\nL 453.915598 36.877566 \r\nL 454.156506 38.2468 \r\nL 454.397415 37.790426 \r\nL 454.638323 37.790454 \r\nL 454.879232 38.246884 \r\nL 455.120141 36.877709 \r\nL 455.361049 38.246942 \r\nL 455.601958 37.790572 \r\nL 455.842866 37.790602 \r\nL 456.083775 38.247053 \r\nL 456.324684 36.877852 \r\nL 456.565592 38.247172 \r\nL 456.806501 37.790848 \r\nL 457.047409 37.790904 \r\nL 457.288318 38.247687 \r\nL 457.529227 36.878 \r\nL 457.770135 38.248434 \r\nL 458.011044 37.79239 \r\nL 458.251952 37.792663 \r\nL 458.492861 38.252237 \r\nL 458.73377 36.878176 \r\nL 458.974678 38.257619 \r\nL 459.215587 37.803215 \r\nL 459.456495 37.805 \r\nL 459.697404 38.284413 \r\nL 459.938313 36.878538 \r\nL 460.179221 38.321348 \r\nL 460.42013 37.877035 \r\nL 460.661038 37.888936 \r\nL 460.901947 38.501641 \r\nL 461.142856 36.880113 \r\nL 461.383764 38.746765 \r\nL 461.624673 38.365709 \r\nL 461.865581 38.44364 \r\nL 462.10649 39.927963 \r\nL 462.347399 36.889423 \r\nL 462.588307 41.516492 \r\nL 462.829216 41.52386 \r\nL 463.070124 42.021841 \r\nL 463.311033 49.051755 \r\nL 463.551942 36.945699 \r\nL 463.79285 59.006135 \r\nL 464.274667 64.235344 \r\nL 464.515576 104.703143 \r\nL 464.756485 37.254457 \r\nL 464.997393 162.637569 \r\nL 465.337223 181 \r\nM 465.868269 181 \r\nL 465.961028 38.535371 \r\nL 466.013663 181 \r\nM 467.145039 181 \r\nL 467.165571 40.836536 \r\nL 467.178846 181 \r\nM 468.362685 181 \r\nL 468.370114 38.028991 \r\nL 468.376182 181 \r\nM 469.569107 181 \r\nL 469.574657 37.034803 \r\nL 469.580795 181 \r\nM 470.77007 181 \r\nL 470.7792 43.59377 \r\nL 470.792383 181 \r\nM 471.953118 181 \r\nL 471.983743 42.54871 \r\nL 472.035876 181 \r\nM 473.038351 181 \r\nL 473.188286 40.68852 \r\nL 473.429194 163.334433 \r\nL 473.670103 89.920084 \r\nL 474.15192 80.191625 \r\nL 474.392829 40.13235 \r\nL 474.633737 61.719342 \r\nL 474.874646 48.922079 \r\nL 475.115554 47.986521 \r\nL 475.356463 47.591985 \r\nL 475.597372 40.023155 \r\nL 475.83828 44.588672 \r\nL 476.079189 42.1722 \r\nL 476.320097 42.023998 \r\nL 476.561006 42.345063 \r\nL 476.801915 40.004886 \r\nL 477.042823 41.877414 \r\nL 477.283732 41.115191 \r\nL 477.52464 41.092444 \r\nL 477.765549 41.532338 \r\nL 478.006458 40.002109 \r\nL 478.247366 41.46139 \r\nL 478.488275 40.954216 \r\nL 478.729183 40.950834 \r\nL 478.970092 41.409733 \r\nL 479.211001 40.001801 \r\nL 479.451909 41.399357 \r\nL 479.692818 40.930541 \r\nL 479.933726 40.930083 \r\nL 480.174635 41.392039 \r\nL 480.415544 40.001877 \r\nL 480.656452 41.390677 \r\nL 480.897361 40.927393 \r\nL 481.138269 40.927361 \r\nL 481.379178 41.389831 \r\nL 481.620087 40.002011 \r\nL 481.860995 41.389737 \r\nL 482.101904 40.927166 \r\nL 482.342812 40.92719 \r\nL 482.583721 41.389749 \r\nL 482.82463 40.002154 \r\nL 483.065538 41.389802 \r\nL 483.306447 40.927291 \r\nL 483.547355 40.92732 \r\nL 483.788264 41.389889 \r\nL 484.029173 40.002299 \r\nL 484.270081 41.389949 \r\nL 484.51099 40.927443 \r\nL 484.751898 40.927474 \r\nL 484.992807 41.390077 \r\nL 485.233716 40.002445 \r\nL 485.474624 41.390228 \r\nL 485.715533 40.927784 \r\nL 485.956441 40.927852 \r\nL 486.19735 41.390923 \r\nL 486.438259 40.002596 \r\nL 486.679167 41.391931 \r\nL 486.920076 40.929854 \r\nL 487.160984 40.930214 \r\nL 487.401893 41.397066 \r\nL 487.642802 40.002785 \r\nL 487.88371 41.404299 \r\nL 488.124619 40.944381 \r\nL 488.365527 40.946766 \r\nL 488.606436 41.440189 \r\nL 488.847345 40.003222 \r\nL 489.088253 41.489543 \r\nL 489.329162 41.042977 \r\nL 489.57007 41.058842 \r\nL 489.810979 41.729967 \r\nL 490.051888 40.005271 \r\nL 490.292796 42.056344 \r\nL 490.533705 41.693416 \r\nL 490.774613 41.796998 \r\nL 491.015522 43.626121 \r\nL 491.256431 40.017544 \r\nL 491.497339 45.733107 \r\nL 491.738248 45.879836 \r\nL 491.979156 46.538397 \r\nL 492.220065 55.693821 \r\nL 492.460974 40.091171 \r\nL 492.701882 68.797478 \r\nL 493.183699 75.71374 \r\nL 493.424608 128.474625 \r\nL 493.665517 40.484434 \r\nL 493.87334 181 \r\nM 494.799297 181 \r\nL 494.87006 42.000525 \r\nL 494.910785 181 \r\nM 496.058094 181 \r\nL 496.074603 44.073642 \r\nL 496.085588 181 \r\nM 497.272523 181 \r\nL 497.279146 40.250113 \r\nL 497.284799 181 \r\nM 498.478137 181 \r\nL 498.483689 41.255279 \r\nL 498.490117 181 \r\nM 499.677906 181 \r\nL 499.688232 46.982496 \r\nL 499.703626 181 \r\nM 500.855277 181 \r\nL 500.892775 45.293256 \r\nL 500.957672 181 \r\nM 501.907384 181 \r\nL 502.097318 43.667636 \r\nL 502.338226 137.881521 \r\nL 502.579135 81.398767 \r\nL 503.060952 73.973313 \r\nL 503.301861 43.226163 \r\nL 503.542769 59.908121 \r\nL 503.783678 50.098414 \r\nL 504.024586 49.389957 \r\nL 504.265495 49.204536 \r\nL 504.506404 43.142427 \r\nL 504.747312 46.938203 \r\nL 504.988221 44.999 \r\nL 505.229129 44.887452 \r\nL 505.470038 45.249022 \r\nL 505.710947 43.128631 \r\nL 505.951855 44.89771 \r\nL 506.192764 44.204442 \r\nL 506.433672 44.187393 \r\nL 506.674581 44.638938 \r\nL 506.91549 43.126576 \r\nL 507.156398 44.585873 \r\nL 507.397307 44.083958 \r\nL 507.638215 44.081444 \r\nL 507.879124 44.547361 \r\nL 508.120033 43.126383 \r\nL 508.360941 44.539676 \r\nL 508.60185 44.0664 \r\nL 508.842758 44.06607 \r\nL 509.083667 44.53431 \r\nL 509.324576 43.126477 \r\nL 509.565484 44.533339 \r\nL 509.806393 44.064146 \r\nL 510.047301 44.064133 \r\nL 510.28821 44.532767 \r\nL 510.529119 43.126616 \r\nL 510.770027 44.532724 \r\nL 511.010936 44.064039 \r\nL 511.251844 44.064065 \r\nL 511.492753 44.532767 \r\nL 511.733662 43.126762 \r\nL 511.97457 44.532824 \r\nL 512.215479 44.064176 \r\nL 512.456387 44.064205 \r\nL 512.697296 44.532913 \r\nL 512.938205 43.126909 \r\nL 513.179113 44.532977 \r\nL 513.420022 44.064337 \r\nL 513.66093 44.064371 \r\nL 513.901839 44.533137 \r\nL 514.142747 43.127057 \r\nL 514.383656 44.533342 \r\nL 514.624565 44.06479 \r\nL 514.865473 44.064878 \r\nL 515.106382 44.534337 \r\nL 515.34729 43.127213 \r\nL 515.588199 44.535779 \r\nL 515.829108 44.067729 \r\nL 516.070016 44.068233 \r\nL 516.310925 44.543094 \r\nL 516.551833 43.127421 \r\nL 516.792742 44.553348 \r\nL 517.033651 44.088293 \r\nL 517.274559 44.091653 \r\nL 517.515468 44.604034 \r\nL 517.756376 43.127978 \r\nL 517.997285 44.673549 \r\nL 518.238194 44.227098 \r\nL 518.479102 44.249387 \r\nL 518.720011 45.0114 \r\nL 518.960919 43.130791 \r\nL 519.201828 45.469201 \r\nL 519.442737 45.13907 \r\nL 519.683645 45.284047 \r\nL 519.924554 47.665837 \r\nL 520.165462 43.14781 \r\nL 520.406371 50.606605 \r\nL 520.64728 50.977475 \r\nL 520.888188 51.892975 \r\nL 521.129097 64.445127 \r\nL 521.370005 43.248685 \r\nL 521.610914 82.546322 \r\nL 522.092731 92.071225 \r\nL 522.33364 164.087194 \r\nL 522.574548 43.767646 \r\nL 522.723983 181 \r\nM 523.727203 181 \r\nL 523.779091 45.571055 \r\nL 523.809532 181 \r\nM 524.970621 181 \r\nL 524.983634 47.098457 \r\nL 524.992624 181 \r\nM 526.182242 181 \r\nL 526.188177 42.482319 \r\nL 526.193525 181 \r\nM 527.38701 181 \r\nL 527.39272 45.849816 \r\nL 527.399687 181 \r\nM 528.585024 181 \r\nL 528.597263 50.132652 \r\nL 528.616153 181 \r\nM 529.753514 181 \r\nL 529.801806 48.002173 \r\nL 529.886826 181 \r\nM 530.633098 181 \r\nL 530.765441 174.541281 \r\nL 531.006349 46.655874 \r\nL 531.247258 115.48218 \r\nL 531.488167 74.194037 \r\nL 531.969984 68.866269 \r\nL 532.210892 46.323287 \r\nL 532.451801 58.705598 \r\nL 532.69271 51.520551 \r\nL 532.933618 51.011639 \r\nL 533.174527 51.012669 \r\nL 533.415435 46.262372 \r\nL 533.656344 49.390598 \r\nL 533.897253 47.86638 \r\nL 534.138161 47.786766 \r\nL 534.37907 48.184586 \r\nL 534.619978 46.252504 \r\nL 534.860887 47.934392 \r\nL 535.101796 47.300114 \r\nL 535.342704 47.288008 \r\nL 535.583613 47.750506 \r\nL 535.824521 46.25108 \r\nL 536.06543 47.712928 \r\nL 536.306339 47.214716 \r\nL 536.547247 47.212951 \r\nL 536.788156 47.685778 \r\nL 537.029064 46.250986 \r\nL 537.269973 47.680412 \r\nL 537.510882 47.202433 \r\nL 537.75179 47.202215 \r\nL 537.992699 47.676722 \r\nL 538.233607 46.251098 \r\nL 538.474516 47.676083 \r\nL 538.715425 47.200943 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"cell_type": "markdown",
"source": "## Benchmark"
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"source": "f2!(dv, v, u, p, t) = ((g, l) = p; dv[1] = -(g/l)*sin(u[1]))\n\np = (g, l) = (9.80665, 1.0)\nymax = 0.9999\nv0 = [√(g/l)*2ymax]\nu0 = [0.0]\ntspan = (0.0, 30.0)\n\ndt = 0.1",
"execution_count": 22,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 22,
"data": {
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"source": "Explicit_RungeKutta = [\n # Euler\n Midpoint\n Heun\n Ralston\n RK4\n BS3\n OwrenZen3\n OwrenZen4\n OwrenZen5\n DP5\n Tsit5\n # Anas5\n FRK65\n PFRK87\n # RKO65\n TanYam7\n DP8\n TsitPap8\n Feagin10\n Feagin12\n Feagin14\n BS5\n Vern6\n Vern7\n Vern8\n Vern9\n]",
"execution_count": 23,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 23,
"data": {
"text/plain": "23-element Vector{Type}:\n Midpoint\n Heun\n Ralston\n RK4\n BS3\n OwrenZen3\n OwrenZen4\n OwrenZen5\n DP5\n Tsit5\n FRK65\n PFRK87\n TanYam7\n DP8\n TsitPap8\n Feagin10\n Feagin12\n Feagin14\n BS5\n Vern6\n Vern7\n Vern8\n Vern9"
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},
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"cell_type": "markdown",
"source": "See also https://diffeq.sciml.ai/stable/solvers/ode_solve/"
},
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"source": "for integrator in Explicit_RungeKutta\n soode_prob = SecondOrderODEProblem(f2!, v0, u0, tspan, p)\n sol = solve(soode_prob, integrator())\n @printf \"%28s:\" integrator\n @time sol = solve(soode_prob, integrator())\n plot_pendulum(sol, ymax; title=\"$integrator()\") |> display\nend",
"execution_count": 24,
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"text/plain": "PyPlot.Figure(PyObject <Figure size 800x250 with 2 Axes>)",
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},
"metadata": {}
},
{
"output_type": "stream",
"text": " Midpoint: 0.001479 seconds (16.75 k allocations: 1.762 MiB)\n Heun: 0.001125 seconds (15.79 k allocations: 1.672 MiB)\n Ralston: 0.001233 seconds (16.77 k allocations: 1.764 MiB)\n RK4: 0.000428 seconds (2.06 k allocations: 219.203 KiB)\n BS3: 0.000290 seconds (2.60 k allocations: 271.969 KiB)\n OwrenZen3: 0.000636 seconds (7.94 k allocations: 825.234 KiB)\n OwrenZen4: 0.000323 seconds (3.73 k allocations: 392.547 KiB)\n OwrenZen5: 0.000611 seconds (3.17 k allocations: 327.203 KiB)\n DP5: 0.000168 seconds (1.23 k allocations: 130.766 KiB)\n Tsit5: 0.000226 seconds (1.98 k allocations: 208.984 KiB)\n FRK65: 7.280693 seconds (21.00 M allocations: 2.050 GiB, 69.38% gc time)\n PFRK87: 2.286901 seconds (7.00 M allocations: 710.817 MiB)\n TanYam7: 0.000217 seconds (713 allocations: 74.141 KiB)\n DP8: 0.000419 seconds (1.16 k allocations: 118.516 KiB)\n TsitPap8: 0.000159 seconds (540 allocations: 58.547 KiB)\n Feagin10: 0.000236 seconds (612 allocations: 66.859 KiB)\n Feagin12: 0.000178 seconds (664 allocations: 75.797 KiB)\n Feagin14: 0.000355 seconds (750 allocations: 90.844 KiB)\n BS5: 0.000158 seconds (1.50 k allocations: 156.688 KiB)\n Vern6: 0.000221 seconds (2.04 k allocations: 211.516 KiB)\n Vern7: 0.000236 seconds (2.05 k allocations: 215.609 KiB)\n Vern8: 0.000193 seconds (1.70 k allocations: 184.609 KiB)\n Vern9: 0.000329 seconds (1.58 k allocations: 176.250 KiB)\n",
"name": "stdout"
},
{
"output_type": "stream",
"text": "┌ Warning: Interrupted. Larger maxiters is needed.\n└ @ SciMLBase C:\\Users\\genkuroki\\.julia\\packages\\SciMLBase\\grNUR\\src\\integrator_interface.jl:331\n┌ Warning: Interrupted. Larger maxiters is needed.\n└ @ SciMLBase C:\\Users\\genkuroki\\.julia\\packages\\SciMLBase\\grNUR\\src\\integrator_interface.jl:331\n┌ Warning: Interrupted. Larger maxiters is needed.\n└ @ SciMLBase C:\\Users\\genkuroki\\.julia\\packages\\SciMLBase\\grNUR\\src\\integrator_interface.jl:331\n┌ Warning: Interrupted. Larger maxiters is needed.\n└ @ SciMLBase C:\\Users\\genkuroki\\.julia\\packages\\SciMLBase\\grNUR\\src\\integrator_interface.jl:331\n",
"name": "stderr"
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "RKN_integrator = [\n Nystrom4\n IRKN3\n IRKN4\n ERKN4\n ERKN5\n Nystrom4VelocityIndependent\n Nystrom5VelocityIndependent\n DPRKN6\n DPRKN8\n DPRKN12\n]",
"execution_count": 25,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 25,
"data": {
"text/plain": "10-element Vector{DataType}:\n Nystrom4\n IRKN3\n IRKN4\n ERKN4\n ERKN5\n Nystrom4VelocityIndependent\n Nystrom5VelocityIndependent\n DPRKN6\n DPRKN8\n DPRKN12"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "See https://diffeq.sciml.ai/stable/solvers/dynamical_solve/"
},
{
"metadata": {
"scrolled": false,
"trusted": true
},
"cell_type": "code",
"source": "for integrator in RKN_integrator\n soode_prob = SecondOrderODEProblem(f2!, v0, u0, tspan, p)\n sol = solve(soode_prob, integrator(); dt=0.1)\n @printf \"%28s:\" integrator\n @time sol = solve(soode_prob, integrator(); dt)\n plot_pendulum(sol, ymax; title=\"$integrator(dt=$dt)\") |> display\nend",
"execution_count": 26,
"outputs": [
{
"output_type": "display_data",
"data": {
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"
},
"metadata": {}
},
{
"output_type": "stream",
"text": " Nystrom4: 0.000207 seconds (2.15 k allocations: 215.594 KiB)\n IRKN3: 0.000135 seconds (2.15 k allocations: 215.906 KiB)\n IRKN4: 0.000183 seconds (2.17 k allocations: 217.141 KiB)\n ERKN4: 0.000061 seconds (558 allocations: 57.750 KiB)\n ERKN5: 0.000080 seconds (642 allocations: 65.703 KiB)\n Nystrom4VelocityIndependent: 0.000173 seconds (2.15 k allocations: 215.422 KiB)\n Nystrom5VelocityIndependent: 0.000144 seconds (2.16 k allocations: 216.266 KiB)\n DPRKN6: 0.000124 seconds (1.34 k allocations: 143.172 KiB)\n DPRKN8: 0.000074 seconds (599 allocations: 63.734 KiB)\n DPRKN12: 0.000073 seconds (345 allocations: 41.312 KiB)\n",
"name": "stdout"
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "symplectic_integrator = [\n SymplecticEuler\n VelocityVerlet\n VerletLeapfrog\n PseudoVerletLeapfrog\n McAte2\n Ruth3\n McAte3\n CandyRoz4\n McAte4\n CalvoSanz4\n McAte42\n McAte5\n Yoshida6\n KahanLi6\n McAte8\n KahanLi8\n SofSpa10\n]",
"execution_count": 27,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 27,
"data": {
"text/plain": "17-element Vector{DataType}:\n SymplecticEuler\n VelocityVerlet\n VerletLeapfrog\n PseudoVerletLeapfrog\n McAte2\n Ruth3\n McAte3\n CandyRoz4\n McAte4\n CalvoSanz4\n McAte42\n McAte5\n Yoshida6\n KahanLi6\n McAte8\n KahanLi8\n SofSpa10"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "See https://diffeq.sciml.ai/stable/solvers/dynamical_solve/"
},
{
"metadata": {
"scrolled": false,
"trusted": true
},
"cell_type": "code",
"source": "for integrator in symplectic_integrator\n soode_prob = SecondOrderODEProblem(f2!, v0, u0, tspan, p)\n sol = solve(soode_prob, integrator(); dt=0.1)\n @printf \"%28s:\" integrator\n @time sol = solve(soode_prob, integrator(); dt)\n plot_pendulum(sol, ymax; title=\"$integrator(dt=$dt)\") |> display\nend",
"execution_count": 28,
"outputs": [
{
"output_type": "display_data",
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"
},
"metadata": {}
},
{
"output_type": "stream",
"text": " SymplecticEuler: 0.000120 seconds (2.14 k allocations: 214.891 KiB)\n VelocityVerlet: 0.000113 seconds (2.14 k allocations: 214.906 KiB)\n VerletLeapfrog: 0.000127 seconds (2.14 k allocations: 214.984 KiB)\n PseudoVerletLeapfrog: 0.000142 seconds (2.14 k allocations: 214.984 KiB)\n McAte2: 0.000178 seconds (2.17 k allocations: 215.672 KiB)\n Ruth3: 0.000145 seconds (2.15 k allocations: 215.312 KiB)\n McAte3: 0.000203 seconds (2.14 k allocations: 215.000 KiB)\n CandyRoz4: 0.000171 seconds (2.15 k allocations: 215.281 KiB)\n McAte4: 0.000180 seconds (2.14 k allocations: 215.094 KiB)\n CalvoSanz4: 0.000191 seconds (2.14 k allocations: 215.125 KiB)\n McAte42: 0.000156 seconds (2.14 k allocations: 215.125 KiB)\n McAte5: 0.000171 seconds (2.14 k allocations: 215.203 KiB)\n Yoshida6: 0.000163 seconds (2.14 k allocations: 215.234 KiB)\n KahanLi6: 0.000173 seconds (2.14 k allocations: 215.375 KiB)\n McAte8: 0.000217 seconds (2.14 k allocations: 215.625 KiB)\n KahanLi8: 0.000219 seconds (2.14 k allocations: 215.750 KiB)\n SofSpa10: 0.000382 seconds (2.14 k allocations: 216.562 KiB)\n",
"name": "stdout"
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "",
"execution_count": null,
"outputs": []
}
],
"metadata": {
"@webio": {
"lastKernelId": null,
"lastCommId": null
},
"_draft": {
"nbviewer_url": "https://gist.github.com/b3caaecf5d1abb2b5646a1550c5601c4"
},
"gist": {
"id": "b3caaecf5d1abb2b5646a1550c5601c4",
"data": {
"description": "Simple gravity pendulum",
"public": true
}
},
"kernelspec": {
"name": "julia-1.7-depwarn-o3",
"display_name": "Julia 1.7.0-DEV depwarn -O3",
"language": "julia"
},
"language_info": {
"file_extension": ".jl",
"name": "julia",
"mimetype": "application/julia",
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},
"toc": {
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"number_sections": true,
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"title_cell": "Table of Contents",
"title_sidebar": "Contents",
"toc_cell": true,
"toc_position": {},
"toc_section_display": true,
"toc_window_display": false
}
},
"nbformat": 4,
"nbformat_minor": 4
}