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Question: pdsolve gives wrong solution to standard wave PDE in 1D

Question:pdsolve gives wrong solution to standard wave PDE in 1D

nm 8552 Maple 2019
pde pdsolve differential-equations physics
September 23 2019
1

Fyi, this solution to 1D wave pde is wrong. The solution does not even satisfy the PDE itself. Compared it to a numerical solution and they are not the same solution. Do not have time now to write the hand solution. But it is clear the solution is not valid.

I do not know now how to roll back to earlier version of the Physcis packages to see if this used to work OK before. Since when typing Physics:-Version(420) It gives error

Error, (in Physics:-Version) unable to determine the Physics Updates version, could you please report the problem to support@maplesoft.com

And Physics:-Version(425) seems to hang. I am not sure if these commands are supposed to automatically download the physics package from the cloud and install it on my PC or what.

Any way, could someone please verify the solution they get is the same as shown below? May be someone with earlier physics package could try to see if they get different solution?

> 

restart
> 

Physics:-Version()

`The "Physics Updates" version in the MapleCloud is 429 and is the same as the version installed in this computer, created 2019, September 23, 0:14 hours, found in the directory C:\Users\me\maple\toolbox\2019\Physics Updates\lib\`

> 

pde:=diff(u(x,t),t$2)=4*diff(u(x,t),x$2);
ic:=u(x,0)=0,D[2](u)(x,0)=sin(x)^2;
bc:=u(-Pi,t)=0,u(Pi,t)=0;
sol:=pdsolve([pde,ic,bc],u(x,t))

diff(diff(u(x, t), t), t) = 4*(diff(diff(u(x, t), x), x))

u(x, 0) = 0, (D[2](u))(x, 0) = sin(x)^2

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

u(x, t) = t*sin(x)^2

> 

pdetest(sol,pde)

-8*t*(2*cos(x)^2-1)

> 

simplify(diff(rhs(sol),t$2)-4*diff(rhs(sol),x$2))

-16*t*cos(x)^2+8*t

> 

 


 

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