Best numerical scheme for MHD wave equations
I am working on a code to solve the linear MHD equations. Until now I have been using McCormack's method, but I would like to try some higher order schemes to see if they work better for my particular problem (waves in a media with discontinuous density changes; I get Gibbs oscillations at the discontinuity boundaries). Right now I am trying to implement a scheme with centered differences for spatial discretization and 3rd order Runge-Kutta for time advance, but I would be grateful if you could suggest a more appropriate scheme. For the moment I am avoiding finite volume methods as they would highly complicate the code...
Thanks in advance!
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