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May 31, 2016 at 15:36 comment added user20536 The reformulation you suggest is a great idea that I will try as soon as possible
May 31, 2016 at 14:20 comment added Peter Frolkovič If you initial functions do not fulfill the stationary PDE as suggested by David, it makes no sense to use explicit method. To address it I added several explanation to my answer. I suggest you "reformulate" your origin problem as one stationary PDE and one (any of two) nonstationary PDE. Good luck!
May 31, 2016 at 14:17 history edited Peter Frolkovič CC BY-SA 3.0
Added more information also to address a suggestion in the comment
May 31, 2016 at 10:06 comment added user20536 Thank you very much for this very detailed answer. If this is really hopeless I may test the explicit method, just to try.
May 30, 2016 at 21:45 history answered Peter Frolkovič CC BY-SA 3.0