# Nonlinear derivative in finite difference

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 February 23, 2021, 08:24 Nonlinear derivative in finite difference #1 New Member   Box Join Date: Feb 2021 Posts: 4 Rep Power: 4 How to write this in finite difference? k.jpeg

 February 23, 2021, 09:24 #2 New Member   Join Date: Feb 2021 Posts: 13 Rep Power: 4 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? BoxQwerty likes this.

February 23, 2021, 12:49
#3
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Filippo Maria Denaro
Join Date: Jul 2010
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Quote:
 Originally Posted by BoxQwerty How to write this in finite difference? Attachment 82923

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.

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