
Solving PDEs
Hi,
Given a PDE of this form
http://i661.photobucket.com/albums/u...U/Capture1.jpg
then one way to solve it iteratively is
http://i661.photobucket.com/albums/u.../Capture7.jpg
(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 :confused:.
Anyone familiar with this who can enlighten me?
Thanks.

Re: Solving PDEs
Hey algorithm.
What is the definition of u_j given in your book?

Re: Solving PDEs
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.

Re: Solving PDEs
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)?