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-   -   stability condition for 4th order of CD (https://www.cfd-online.com/Forums/main/14958-stability-condition-4th-order-cd.html)

 qunwuhe@hotmail.com March 20, 2008 22:30

stability condition for 4th order of CD

what is the stability condition for 4th oder of central difference for diffusion equation?

for 2th, is delta t < delta x^2 is it delta t < delta x^4?

 Mohamed April 20, 2008 17:35

Re: stability condition for 4th order of CD

Hello ,

To get the stability condition you can perform if you are using a linear scheme ( which is obviously the case ) , a von neumann analysis, i.e., you inject a fourier in your scheme

Fourier mode : ------------

u(xj,tn) = A(k)^n *exp(2*i*pi*k*xj)

where xj = j*dx and tn = n*dt and k is the wave vector (variable in fourier space)

Stability condition : -------------------

Then the stability condition is |A(k)| < 1 . You have then to determine the relationship between dx , nu and dt to satisfy the stability condition.

It is a simple computatio that you can do by hands in 1D.

Best regards, Mohamed.

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