Question: Solving and Plotting PDE

Having difficulties solving pde. Below is the problem and its not plotting. Anyone with useful informations. Please

restart;
with(PDEtools, casesplit, declare);
with(DEtools, gensys);
with(Physics);

PDE := diff(theta(x, t), x, x)+beta*theta(x, t)*(diff(theta(x, t), x, x))+beta*((diff(theta(x, t), x))^2)-M^2*theta(x, t)-S[h]*(theta(x, t)^2)+M^2*G*(1+E*theta(x, t))-P[e]*(diff(theta(x, t), x)) = diff(theta(x, t), t);
/ d  / d             \\
|--- |--- theta(x, t)||
\ dx \ dx            //

                      / d  / d             \\
   + beta theta(x, t) |--- |--- theta(x, t)||
                      \ dx \ dx            //

                           2                                     
          / d             \     2                               2
   + beta |--- theta(x, t)|  - M  theta(x, t) - S[h] theta(x, t) 
          \ dx            /                                      

      2                              / d             \    d  
   + M  G (1 + E theta(x, t)) - P[e] |--- theta(x, t)| = --- 
                                     \ dx            /    dt 

  theta(x, t)
BC := theta(x, 0) = 0, Dt(theta(0, t)) = 0, theta(1, t) = 1;
     theta(x, 0) = 0, Dt(theta(0, t)) = 0, theta(1, t) = 1
Codes := [beta = .1, M = .1, S[h] = .1, G = .1, P[e] = .1, E = .1];
S1 := pdsolve({BC, subs(Codes, PDE)});
PDEplot(S1, [[t, theta(x, t)], [x, theta(x, t)]], t = 0 .. 1, x = 0 .. 1, iterations = 2, numchar = [10, 10], stepsize = 0.5e-1, numsteps = [-5, 5]);
   PDEplot([[t, theta(x, t)], [x, theta(x, t)]], t = 0 .. 1, 

     x = 0 .. 1, iterations = 2, numchar = [10, 10], 

     stepsize = 0.05, numsteps = [-5, 5])

 

Please Wait...