From 0b3ea2abe50f06188bcdb2f57c76361f57b2be5d Mon Sep 17 00:00:00 2001 From: termi-official Date: Wed, 29 Mar 2023 21:14:00 +0200 Subject: [PATCH] Fix PIDE docs. --- docs/src/tutorials/PIDE.md | 9 ++++++++- 1 file changed, 8 insertions(+), 1 deletion(-) diff --git a/docs/src/tutorials/PIDE.md b/docs/src/tutorials/PIDE.md index 260358f66..3b6057728 100644 --- a/docs/src/tutorials/PIDE.md +++ b/docs/src/tutorials/PIDE.md @@ -3,21 +3,28 @@ It is also possible to solve PIDEs with MethodOfLines.jl. Consider the following system: + ```math \frac{\partial}{\partial t}u(t, x)+2u(t, x)+5\frac{\partial}{\partial x}[\int_0^xu(t, x)dx]=1 ``` + On the domain: + ```math t \in (0, 2) x \in (0, 2\pi) ``` + With BCs and ICs: + ```math u(0, x)=cos(x) \frac{\partial}{\partial x}u(t, 0)=0 \frac{\partial}{\partial x}u(t, 2)=0 ``` + We can discretize such a system like this: + ```@example pide using MethodOfLines, ModelingToolkit, OrdinaryDiffEq, DomainSets, Plots @@ -92,4 +99,4 @@ tdisc = sol[t] integralsol = sol[integral(t, x)] heatmap(integralsol) -``` \ No newline at end of file +```