Nonlinear system of algebraic equations

[cesarmv]

Hello,

It's my first topic here. :)
In order to solve a PDE numerically, I have reached in a nonlinear system of algebraic equations. Does anyone here know a good method to solve it numerically?

It seems like this:

x_ij (t+dt) is proportional to x_i,j+1(t), x_ij²(t), x_i,j-1²(t), x_i-1,j(t), x_i+1,j(t), etc..

where i and j are 'coordinates' of a 2D grid.

Thank you so much in advance.



César.

 

[hotvette]

If partial derivatives are straightforward to calculate, Newton's Method is a classic choice:

http://www.math.ohiou.edu/courses/math344/lecture13.pdf

 

[cesarmv]

Ok, I'll take a look, thanks!