# stability condition for 4th order of CD

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 March 20, 2008, 22:30 stability condition for 4th order of CD #1 qunwuhe@hotmail.com Guest   Posts: n/a 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?

 April 20, 2008, 17:35 Re: stability condition for 4th order of CD #2 Mohamed Guest   Posts: n/a 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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