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Question: pdsolve/numeric/process_PDEs) can only numerically solve PDE with two independent

Question:pdsolve/numeric/process_PDEs) can only numerically solve PDE with two independent

Cresta 0 Maple
range
April 04 2011
0 
> restart;
> with(DifferentialGeometry):with(LinearAlgebra):with(JetCalculus):with(Tools):with(PDEtools): with(DEtools):
> 
> declare(u(x(t),y(t),t),v(x(t),y(t),t));

             u(x(t), y(t), t) will now be displayed as u


                   x(t) will now be displayed as x


                   y(t) will now be displayed as y


             v(x(t), y(t), t) will now be displayed as v

> PDE_sys:={diff(u(x,y,t),t) = B+(u(x,y,t)^2)*v(x,y,t)+(A+1)*u(x,y,t)+alpha*(diff(u(x,y,t),x,x) + diff(u(x,y,t),y,y)),                                 diff(v(x,y,t),t) =A*u(x,y,t)-(u(x,y,t)^2)*v(x,y,t)+beta*(diff(v(x,y,t),x,x) + diff(v(x,y,t),y,y))};

                                   2
  PDE_sys := {u[t] = B + u(x, y, t)  v(x, y, t) + (A + 1) u(x, y, t)

         + alpha (u[x, x] + u[y, y]), v[t] = A u(x, y, t)

                     2
         - u(x, y, t)  v(x, y, t) + beta (v[x, x] + v[y, y])}

> Init := u(x,y,0)=1+rand()*(0.000000000001)*(x+y),v(x,y,0)=1+rand()*(0.000000000001)*(x+y);

  Init := u(x, y, 0) = 1 + 0.3957188605 x + 0.3957188605 y,

        v(x, y, 0) = 1 + 0.1931398164 x + 0.1931398164 y

> Bdry := D[1](u(x,y,t))(0,y,t)=0, D[1](u(x,y,t))(l,y,t)=0,D[2](u(x,y,t))(x,0,t)=0,D[2](u(x,y,t))(x,l,t)=0,D[1](v(x,y,t))(0,y,t)=0, D[1](v(x,y,t))(l,y,t)=0,D[2](v(x,y,t))(x,0,t)=0,D[2](v(x,y,t))(x,l,t)=0;

  Bdry := D[1](u(x, y, t))(0, y, t) = 0,

        D[1](u(x, y, t))(l, y, t) = 0, D[2](u(x, y, t))(x, 0, t) = 0,

        D[2](u(x, y, t))(x, l, t) = 0, D[1](v(x, y, t))(0, y, t) = 0,

        D[1](v(x, y, t))(l, y, t) = 0, D[2](v(x, y, t))(x, 0, t) = 0,

        D[2](v(x, y, t))(x, l, t) = 0

> IBC:={u(x,y,0)=1+rand()*(0.000000000001)*(x+y),v(x,y,0)=1+rand()*(0.000000000001)*(x+y),D[1](u(x,y,t))(0,y,t)=0, D[1](u(x,y,t))(l,y,t)=0,D[2](u(x,y,t))(x,0,t)=0,D[2](u(x,y,t))(x,l,t)=0,D[1](v(x,y,t))(0,y,t)=0, D[1](v(x,y,t))(l,y,t)=0,D[2](v(x,y,t))(x,0,t)=0,D[2](v(x,y,t))(x,l,t)=0};

  IBC := {u(x, y, 0) = 1 + 0.02242417046 x + 0.02242417046 y,

        v(x, y, 0) = 1 + 0.8001874845 x + 0.8001874845 y,

        D[1](u(x, y, t))(0, y, t) = 0, D[1](u(x, y, t))(l, y, t) = 0,

        D[1](v(x, y, t))(0, y, t) = 0, D[1](v(x, y, t))(l, y, t) = 0,

        D[2](u(x, y, t))(x, 0, t) = 0, D[2](u(x, y, t))(x, l, t) = 0,

        D[2](v(x, y, t))(x, 0, t) = 0, D[2](v(x, y, t))(x, l, t) = 0}


> paramsl:={l=10,alpha=0.01,beta=0.1};

            paramsl := {l = 10, alpha = 0.01, beta = 0.1}

> PDE_sol := pdsolve(eval(PDE_sys,paramsl),eval(IBC,paramsl),[u,v], numeric, time=t,range=0..100);
Error, (in pdsolve/numeric/process_PDEs) can only numerically solve PDE with two independent variables, got {t, x, y}

> PDE_sol := pdsolve(eval(PDE_sys,paramsl),eval({Init,Bdry},paramsl),[u,v], numeric, time=t,range=0..100);
Error, (in pdsolve/numeric/process_PDEs) can only numerically solve PDE with two independent variables, got {t, x, y}

> PDE_sol := pdsolve(eval(PDE_sys,paramsl),eval({Init,Bdry},paramsl),numeric);
Error, (in pdsolve/numeric/process_PDEs) can only numerically solve PDE with two independent variables, got {t, x, y}

> PDE_sol := pdsolve(PDE_sys,eval(IBC,paramsl),numeric);
Error, (in pdsolve/numeric/process_PDEs) can only numerically solve PDE with two independent variables, got {t, x, y}

> PDE_sol := pdsolve(op(eval([PDE_sys,{IBC}],{l=10,alpha=0.01,beta=0.1})),numeric);
Error, (in pdsolve/numeric/process_PDEs) can only numerically solve PDE with two independent variables, got {t, x, y}

 
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