{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Adaptivity at a singularity"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In {doc}`basics-sing` we found an IVP that appears to blow up in a finite amount of time. Because the solution increases so rapidly as it approaches the blowup, adaptive stepping is required to even get close. In fact it's the failure of adaptivity that is used to get an idea of when the singularity occurs."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"using FundamentalsNumericalComputation"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\u001b[36mODEProblem\u001b[0m with uType \u001b[36mInt64\u001b[0m and tType \u001b[36mFloat64\u001b[0m. In-place: \u001b[36mfalse\u001b[0m\n",
"timespan: (0.0, 1.0)\n",
"u0: 1"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"f = (u,p,t) -> (t+u)^2\n",
"ivp = ODEProblem(f,1,(0.,1.))"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"┌ Warning: Stepsize too small near t=0.785408720407281\n",
"└ @ FundamentalsNumericalComputation /Users/driscoll/.julia/packages/FundamentalsNumericalComputation/bLUG7/src/chapter06.jl:86\n"
]
}
],
"source": [
"t,u = FNC.rk23(ivp,1e-5);"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"\n",
"\n"
],
"text/plain": [
"Plot{Plots.GRBackend() n=1}"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot(t,u,label=\"\",\n",
" xlabel=\"t\",yaxis=(:log10,\"u(t)\"),title=\"Finite-time blowup\")"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia (faststart)",
"language": "julia",
"name": "julia-fast"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.4.1"
}
},
"nbformat": 4,
"nbformat_minor": 4
}