"Rui Ma" <email@example.com> wrote in message <firstname.lastname@example.org>...
> I'm using pdepe to solve a heat equation on 0<r<R and 0<t<L, with time-varying boundary condition T(R, t) = g(t). My questions are as follows:
> (1) is pdepe a full-domain solver? In other words, does the solution T(r, t) depends on the boundary conditions from a future time point t_1 > t?
> (2) if (1) is true, then pdepe is non-causal, and is there a way to implement a causal solver such that the solution of T(r, t) can be updated sequentially, and only depends on boundary conditions from the past g(t_0) where t_0<t?
Don't mix between causal (1st order PDE, such as thermal equation than Cauchy theorem shows it's causal) and implicit numerical scheme where some operator (such as diffusion) and bc is enforced on the next time step and not the current one, requiring PDE toolbox rather ODE solver.