Hi all , i was to enter a semi lagrangian equation in grasshopper , is it possible with scripting or within grasshopper at all ? 
There is no formal equation solver in grasshopper. It is not matlab or mathematica or mapple. So you will have to use a script. And here you can do almost whatever you want.
See reaction diffusion example on old grasshopper forum.
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Thanks laurent , i did checked it out , I did the partials and gradient calculation in the expression component piece by piece
It is most effective to do calculation in a VB/C# component and to add parallel calculations. Expression component is enough if you have no speed problem.
I think i will have speed limits due to my long definition 
, for sure scripting will be required .