Nonlinear derivative in finite difference
 

How to write this in finite difference?

Attachment 82923

first decide which finite difference you need for d/dx. stencil size - number of nodes - one sided or central. then plug in for inner derivative and apply. then plug in for outer derivative and apply. alternative is: work out full terms first, then apply. what is the purpose of this?

If you want to use the divergence form you simply write


0.5*(f(i+1)**3-f(i-1)**3)/h


where f is a vector where you previously computed the discrete derivative du/dx.


Conversely you can expand the derivative in a quasi-linear form.