Thread: Solving PDEs

Hi,

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?

Thanks.

Hey algorithm.

What is the definition of u_j given in your book?

chiro,

Thanks for your reply.

is defined as the numerical approximation of at time index , and distance index . So basically it represents the time iteration and the distance iteration of the solver algorithm.

What is the taylor series expansion look like and how similar is it to your approximation (where dx's, dt's, etc are approximated by delta_x, delta_t etc)?