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Question: Trouble with pdsolve

Question:Trouble with pdsolve

Rouben Rostamian 7711 Maple 2020
pde pdsolve differential-equations
May 09 2020
2

This worksheet shows an unexpected behavior of pdsolve().  It solves the heat equation on the interval (−1,1) but fails on the interval (0,1).  I see no technical reason for this happening — it's probably due to a little bug lurking somewhere.

> 

restart;
> 

kernelopts(version);

`Maple 2020.0, X86 64 LINUX, Mar 4 2020, Build ID 1455132`

> 

Physics:-Version();

`The "Physics Updates" package is not installed`

Solve the heat equation on the interval -1 < x and x < 1 and

boundary conditions u(-1, t) = 0, u(1, t) = 0.

> 

pde := diff(u(x,t),t) = diff(u(x,t),x,x);

diff(u(x, t), t) = diff(diff(u(x, t), x), x)

> 

bc := u(-1,t)=0, u(1,t)=0;

u(-1, t) = 0, u(1, t) = 0

> 

ic := u(x,0) = cos(Pi/2*x);

u(x, 0) = cos((1/2)*Pi*x)

> 

pdsol := expand(pdsolve({pde,bc,ic}));

u(x, t) = cos((1/2)*Pi*x)*exp(-(1/4)*t*Pi^2)

That's good.  Apply pdetest to verify it:

> 

pdetest(pdsol, [pde,bc,ic]);

[0, 0, 0, 0]

Now, solve the same problem on the interval 0 < x and x < 1 and

boundary condition u__x(0, t) = 0 and u(1, t) = 0.  It should be

evident that the solution remains the same as the one calculated

above, due to symmetry, and here is the verification:

> 

bc_new := D[1](u)(0,t)=0, u(1,t)=0;

(D[1](u))(0, t) = 0, u(1, t) = 0

> 

pdetest(pdsol, [pde,bc_new,ic]);

[0, 0, 0, 0]

But for some reason Maple's pdsolve fails to solve the PDE.  Actually

its response is somewhat erratic -- sometimes it returns nothing at all,

and sometimes it exits with an error message.

> 

pdsolve({pde,bc_new,ic});

 

Download pdsolve-fails.mw

 
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