Merge pull request #64 from mikelehu/master

issue 61
SciML · Mar 31, 2024 · 45c7716 · 45c7716
2 parents b19edaa + bf98fef
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diff --git a/Examples/.ipynb_checkpoints/Riccati Differencial Equations-checkpoint.ipynb b/Examples/.ipynb_checkpoints/Riccati Differencial Equations-checkpoint.ipynb
@@ -0,0 +1,236 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "2fb54ab2",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "using IRKGaussLegendre\n",
+    "using OrdinaryDiffEq"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "ce474231",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "function x(t)\n",
+    "    u0 = [1.]\n",
+    "    tspan = (1.,t)\n",
+    "    prob = ODEProblem(Ric1ODE!, u0, tspan)\n",
+    "    sol = solve(prob, Tsit5(); reltol = 1.e-10, abstol = 1.e-10, save_everystep = false)\n",
+    "    return sol(t)\n",
+    "end\n",
+    "\n",
+    "function Ric1ODE!(du, u, pars, t) \n",
+    "    du[1] = -2u[1]-1+u[1]^2\n",
+    "end"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "4c16810d",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "f(u, p, t) = x(t)[1]^2\n",
+    "\n",
+    "function f1!(du, u, pars, t)\n",
+    "    du[1] = pars(t)\n",
+    "end\n",
+    "\n",
+    "u0 = [0.]; u00 = 0.;\n",
+    "tspan = (0.0, 1.0)\n",
+    "pars = t->x(t)[1]^2\n",
+    "prob = ODEProblem(f, u00, tspan)\n",
+    "prob1 = ODEProblem(f1!, u0, tspan, pars)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "edd522be",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "sol1 = solve(prob1, Tsit5(), reltol = 1e-8, abstol = 1e-8); sol1(1)[1]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "899dbbb7",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "eltype(prob1.tspan)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "dc97f9b9",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "sol2 = solve(prob1, IRKGaussLegendre.IRKGL16(maxtrials=4), dt=1., reltol = 1e-8, abstol = 1e-8); sol2(1)[1]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "5ce7b8ef",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# v 1.10.0 :  3.3006156872882713"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3c71fc4e",
+   "metadata": {},
+   "source": [
+    "## Andreas examples"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "b8ccc3cc",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "sol2 = solve(prob1, IRKGaussLegendre.IRKGL16(), reltol = 1e-8, abstol = 1e-8); sol2(1)[1]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "ab14de53",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "sol2 = solve(prob1, IRKGaussLegendre.IRKGL16(), dt = 1e-7,reltol = 1e-8, abstol = 1e-8); sol2(1)[1]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "50dce94e",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "sol2 = solve(prob1, IRKGaussLegendre.IRKGL16(), dt =1e-6,reltol = 1e-8, abstol = 1e-8); sol2(1)[1]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "fef268bc",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "sol2 = solve(prob1, IRKGaussLegendre.IRKGL16(), dt = 1e-5,reltol = 1e-8, abstol = 1e-8); sol2(1)[1]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "86e473b0",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "sol2 = solve(prob1, IRKGaussLegendre.IRKGL16(), dt = 1e-4,reltol = 1e-8, abstol = 1e-8); sol2(1)[1]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "e15976ba",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "sol2 = solve(prob1, IRKGaussLegendre.IRKGL16(), dt = 1e-3,reltol = 1e-8, abstol = 1e-8); sol2(1)[1]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "fe98afa7",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "sol2 = solve(prob1, IRKGaussLegendre.IRKGL16(), dt = 1e-2,reltol = 1e-8, abstol = 1e-8); sol2(1)[1]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "3f241056",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "sol2 = solve(prob1, IRKGaussLegendre.IRKGL16(), dt = 1e-1,reltol = 1e-8, abstol = 1e-8); sol2(1)[1]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "0d05cf95",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "sol2 = solve(prob1, IRKGaussLegendre.IRKGL16(), dt = 1,reltol = 1e-8, abstol = 1e-8); sol2(1)[1]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "b4a7cf4a",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "sol2 = solve(prob1, IRKGaussLegendre.IRKGL16(), dt = 10,reltol = 1e-8, abstol = 1e-8); sol2(1)[1]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "cd3ee271",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "sol2 = solve(prob1, IRKGaussLegendre.IRKGL16(), dt = 100,reltol = 1e-8, abstol = 1e-8); sol2(1)[1]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "d18c366f",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Julia 1.9.1",
+   "language": "julia",
+   "name": "julia-1.9"
+  },
+  "language_info": {
+   "file_extension": ".jl",
+   "mimetype": "application/julia",
+   "name": "julia",
+   "version": "1.9.1"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}