Mathematica

PDE simplification

  • Here is an example on how to check a PDE with mathematica. Sometimes, one has to use Full Simplify rather than simplify. Here is one possibility to do things 
    f[t_,x_]:=(1/Sqrt[t])*Exp[-x^2/(4t)];
FullSimplify[D[f[t,x],t] == D[f[t,x],{x,2}]]


    Here is the same computation, where the function g is just given as an expression. I was putting a Clear[f] before so that the previous definition would not interfere. 
    Clear[f]; 
f=(1/Sqrt[t])*Exp[-x^2/(4t)];
FullSimplify[D[f,t] == D[f,{x,2}]]


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