Given a PDE of this form
then one way to solve it iteratively is
(Equations from IISc).
The update equation has me confused for the following reason. appears in the PDE as function of both time and distance . However, the update equation only gives you as a function of time ( ), and what's more, it seems to assume that is already known as a function of distance because it has terms.
In short, the solver seems to assume that you already know the solution .
Anyone familiar with this who can enlighten me?