Hi guys,

Maple solved numerically the following system of two coupled PDEs.

PDE1 := diff(a(x,t),t) = - 2*a(x,t) + 1*b(x,t)
- exp(- 1/(1 - (x-0.5)^2))*( diff(a(x,t),x,x) + a(x,t)*diff(b(x,t),x,x) - b(x,t)*diff(a(x,t),x,x) );

PDE2 := diff(b(x,t),t) = - 1*b(x,t) + 2*a(x,t)
- exp(- 1/(1 - (x-0.5)^2))*( diff(b(x,t),x,x) - a(x,t)*diff(b(x,t),x,x) + b(x,t)*diff(a(x,t),x,x) );

IC := [ a(x,0)=exp( - 1/(1 - (x-0.5...

Hi,

I would like to solve the system of PDEs

PDE1 := diff(a(x,t),t) = - 2*a(x,t) + 1*b(x,t)
- 4*( diff(a(x,t),x,x) + a(x,t)*diff(b(x,t),x,x) - b(x,t)*diff(a(x,t),x,x) );

PDE2 := diff(b(x,t),t) = - 1*b(x,t) + 2*a(x,t)
- 4*( diff(b(x,t),x,x) - a(x,t)*diff(b(x,t),x,x) + b(x,t)*diff(a(x,t),x,x) );

subjected to the initial value

IC := [ a(x,0)=exp( (x-0.5)^2 ), b(x,0)=0 ];

If I try to do so by typing

pdsolve([PDE1,PDE2],IC,numeric);