I've been using Mathematica to solve nonlinear partial differential equations for my doctoral research for the last 2 years or so. I am not an expert in Mathematica or mathematics and I am an engineer trying to express thermodynamic and fluid dynamic phenomena through math equations which subsequently need solving using numerical methods!
I find that Mathematica is definitely the way to go and I am a big fan of the
With that short background, here's my question:
If I am to publish numerical results obtained in Mathematica, how should I go about it? I obviously validate my results against previously published data but here is the thing: say we have a non-linear PDE:
h_t + N[h[x,t]]=0 where
N[h[x,t]] is the nonlinear part.
Most scientific publications would mention the method used to solve the equation (Eq: the BDF method, the Newton-Kantorovich method etc.)
When I solve this in Mathematica in a vanilla style without using any
Method options in
NDSolve thus allowing Mathematica to adapt and select it's own method, how do I cite the method? I haven't come across publications that do, so I ask...
I do realize that there is the
Trace option available that allows for the user to figure out what method was used but it isn't very intuitive!
Any suggestions? Inputs?