Nonlinear system of algebraic equations

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To solve a nonlinear system of algebraic equations derived from a partial differential equation (PDE) numerically, a recommended method is Newton's Method, especially when partial derivatives are easily computed. The discussion highlights the relationship between grid coordinates in a 2D space, where the value at a grid point is influenced by its neighboring points. The user expresses gratitude for the suggestion and intends to explore it further.
cesarmv
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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:

xij (t+dt) is proportional to xi,j+1(t), xij2(t), xi,j-12(t), xi-1,j(t), xi+1,j(t), etc..

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

Thank you so much in advance.



César.
 
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Ok, I'll take a look, thanks!
 

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