Math Help - Solving PDEs

1. 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. $u(x, t)$ appears in the PDE as function of both time $t$ and distance $x$. However, the update equation only gives you $u$ as a function of time ( $u^{n+1}_{j}$), and what's more, it seems to assume that $u$ is already known as a function of distance because it has $u^{n}_{j+1}$ terms.

In short, the solver seems to assume that you already know the solution .

Anyone familiar with this who can enlighten me?

Thanks.

2. Re: Solving PDEs

Hey algorithm.

What is the definition of u_j given in your book?

3. Re: Solving PDEs

chiro,

$u^n_{j}$ is defined as the numerical approximation of $u(x, t)$ at time index $n$, and distance index $x$. So basically it represents the $n^{th}$ time iteration and the $j^{th}$ distance iteration of the solver algorithm.