Hello!
I solved a simple PDE numerically and found that I couldn't implement a simple thing!
For example:
restart:
PDE := diff(u(x,t),t)=1/10*diff(u(x,t),x,x);
IBC := {u(x,0)=1, u(0,t)=0, D[1](u)(1,t)=0};
pds := pdsolve(PDE,IBC,numeric);
p1 := pds:-plot(t=0): p2 := pds:-plot(t=1/10):p3 := pds:-plot(t=1/2):p4 := pds:-plot(t=1):
plots[display]({p1,p2,p3,p4});
I got some spatial dependencies for different fixed t. But I want to get opposite! How to get time dependence for fixed x?
Replacing t with x results in an error.
Update.
This equation is example, really I solve this:
PDE := diff(u(x,t),t)+v*(1+k*sin(2*Pi*f*t))*diff(u(x,t),x)=a*diff(u(x,t),x,x);
IBC := {u(x,0)=T__0,u(0,t)=sin(2*Pi*f*t),u(L,t)=T__0};
So sin makes this equation nonlinear, so I need numerical procedure.