Question: Solve numerically a system of PDEs


I am using Maple 11 and trying to solve numerically the following easy system of 1st order, linear PDEs:

> PDE := [diff(u(x, t), t) = v(x, t), diff(v(x, t), x) = u(x, t)];
               [ d                             d                          ]
               [--- u(x, t) = v(x, t), --- v(x, t) = u(x, t) ]
               [ dt                           dx                         ]
> IBC := {u(x, 0) = exp(-x), v(0, t) = exp(t)}:

Indeed, when I try to solve it I get:

> pds := pdsolve(PDE, IBC, [u, v], numeric, time = t, range = -1 .. 0);
Error, (in pdsolve/numeric/match_PDEs_BCs) cannot handle systems with multiple PDE describing the time dependence of the same dependent variable, or having no time dependence

My final aim is to solve a more complicated system of PDEs, however I cannot surely go much further if I cannot even solve this one...

Any suggestions?

Thanks a lot for your attention,


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