# Solving PDEs

• Oct 20th 2012, 03:56 AM
algorithm
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.../Capture-7.jpg

(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 :confused:.

Anyone familiar with this who can enlighten me?

Thanks.
• Oct 20th 2012, 05:46 PM
chiro
Re: Solving PDEs
Hey algorithm.

What is the definition of u_j given in your book?
• Oct 21st 2012, 02:42 AM
algorithm
Re: Solving PDEs
chiro,