Trying Maple on a textbook problem to verify my hand solution.

But Maple pdsolve hangs with the mserver.exe tallomg almost 100% CPU and over 10 GB of RAM!

I waited for almost 20 minutes. Tried another time, same thing.

It is no problem if Maple can't solve this, but Maple seems to suffer from too many hangs when it is not able to solve a problem. I've had similar problems with dsolve also.

This is on windows 10, 64 bit with Maple 2018.2 With Physics updates version 218

restart;
PackageTools:-IsPackageInstalled("Physics Updates");

218

interface(showassumed=0);
infolevel[pdsolve]:=2;
pde := diff(u(x,t),t)=k*diff(u(x,t),x$2)+Q(x,t);
ic := u(x,0)=f(x);
bc := eval(diff(u(x,t),x),x=0)=A(t),eval(diff(u(x,t),x),x=1)=B(t);
sol:=pdsolve({pde,ic,bc},u(x,t)) assuming t>0,k>0;

then

* trying method "_Fn" for 2nd order PDEs
-> trying "linear_in_xt"
-> trying "BC_equal_0"
* trying method "_Cn_cn" for 2nd order PDEs
Trying travelling wave solutions as power series in tanh ...
Trying travelling wave solutions as power series in ln ...
Trying travelling wave solutions as power series in tanh ...
Trying travelling wave solutions as power series in ln ...
* trying method "Wave" for 2nd order PDEs
-> trying "Cauchy"
-> trying "SemiInfiniteDomain"
-> trying "WithSourceTerm"
* trying method "Heat" for 2nd order PDEs
-> trying "SemiInfiniteDomain"
-> trying "WithSourceTerm"
* trying method "Series" for 2nd order PDEs
-> trying "ThreeBCsincos"
-> trying "FourBC"
-> trying "ThreeBC"
-> trying "ThreeBCPeriodic"
-> trying "WithSourceTerm"
* trying method "_Fn" for 2nd order PDEs
-> trying "linear_in_xt"
-> trying "BC_equal_0"
* trying method "_Cn_cn" for 2nd order PDEs

And here is hangs. Notice that because both ends are Neumann, there is no unique solution to this problem. So the solution will contain arbitrary constant. May be this is what made pdsolve hang?

No it is not. Trying with only one end nonhomogeneous Neumann, and the other end Dirichlet, it still hangs. The problem seems to be with one end is nonhomogeneous Neumann, which is a function of time. So this hangs also (same place)

restart;
interface(showassumed=0);
infolevel[pdsolve]:=2;
pde := diff(u(x,t),t)=k*diff(u(x,t),x$2)+Q(x,t);
ic := u(x,0)=f(x);
bc := eval(diff(u(x,t),x),x=0)=A(t),eval(diff(u(x,t),x),x=1)=0;
sol:=pdsolve({pde,ic,bc},u(x,t)) assuming t>0,k>0;

And this also

restart;
interface(showassumed=0);
infolevel[pdsolve]:=2;
pde := diff(u(x,t),t)=k*diff(u(x,t),x$2)+Q(x,t);
ic := u(x,0)=f(x);
bc := eval(diff(u(x,t),x),x=0)=sin(t),eval(diff(u(x,t),x),x=1)=0;
sol:=pdsolve({pde,ic,bc},u(x,t)) assuming t>0,k>0;

But this does not hang

interface(showassumed=0);
infolevel[pdsolve]:=2;
pde := diff(u(x,t),t)=k*diff(u(x,t),x$2)+Q(x,t);
ic := u(x,0)=f(x);
bc := eval(diff(u(x,t),x),x=0)=1,eval(u(x,t),x=1)=0;
sol:=pdsolve({pde,ic,bc},u(x,t)) assuming t>0,k>0;

The issue seems to be when one end is nonhomogeneous Neumann which is function of time.

Is there a workaround so it does not hang? The complaint is that Maple hangs, and not that Maple unable to solve the PDE.