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?
Re: stability condition for 4th order of CD
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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