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?
Thanks very much in advance!