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

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