In the attached
- I removed some "comment" areas which appeared to be a mixture of "comment" and "executable code" - always tricky to tell the difference if you insist on using 2-D input
- I didn't like the syntax for the boundary condition D(u(0, t)) = 0, Slightly surprised that Maple didn't object to this, but I changed it to something which is definitely syntactically correct.
Even then I still get an error that
Error, (in pdsolve/numeric/plot) unable to compute solution for t>HFloat(0.0): matrix is singular
Now I can't be certain why this error message is occurring, but since the problem seems to occur at (x,t)=(0,0), one thing that bothers me is the BCs/ICs at (0,0).
You have the initial condition
u(x, 0) = 0.1*sin(2*Pi*x)
which must be true for all 'x' - so the above requires that u(0,0)=0.
However you also have the boundary condtion
u(0, t) = 0.5*cos(2*Pi*t)
which is true for all 't', so this requires that u(0,0)=0.5 in conflict with initial condition above
A similar conflict occurs with the BCs/ICs for v(0,0): the relevant initial condition has v(0,0)=0, wheres the relevant boundary condition has v(0,0)=0.2
You might want to give some thought to these boundary/initial condition conflicts