# Question:Finding an approximate function for a PDE numerical solution

## Question:Finding an approximate function for a PDE numerical solution

Maple 2015

Are there any commands in maple that will help me find a suitable function that approximates the numerical solution of:

 > restart;   PDE := diff(v(x, t), t) = diff(v(x, t), x, x);   JACOBIINTEGRAL := int(JacobiTheta3(0, exp(-Pi^2*s))*v(1, t-s)^4, s = 0 .. t);   IBC:= D[1](v)(0,t)=0,         D[1](v)(1,t)=-0.000065*v(1, t)^4,         v(x,0)=1; # # For x=0..1, t=0..1, the solution varies only very slowly # so I have increased the timestep/spacestep, just to speed # up results generation for diagnostic purposes #   pds := pdsolve( PDE, [IBC], numeric, time = t, range = 0 .. 1,                   spacestep = 0.1e-1, timestep = 0.1e-1,                   errorest=true                 )
 (1)
 > # # Plot the solution over the ranges x=0..1, # time=0..1. Not a lot happens! #   pds:-plot(x=1, t=0..1);
 > # # Plot the estimated error over the ranges x=0..1, # time=0..1 #   pds:-plot( err(v(x,t)), x=1,t=0..1);
 > # # Get some numerical solution values #   pVal:=pds:-value(v(x,t), output=procedurelist):   for k from 0 by 0.1 to 1 do       pVal(1, k)[2], pVal(1, k)[3];   od;
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 (2)
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