Paulo Baumbach

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First: Is it possible to solve an pde equation/system where bcs are an array or matrix?

Second: Is it possible to get a discrete response in an array/matrix for this pde equation/system?

As an example I applied the heat conduction equation to a bar of 50 cm in length. Initially the bar has a uniform temperature field of 20ºC. The ends are maintained at a temperature of 0°C over time. I fixed a unitary thermal diffusivity.

restart:
k:=1:
pde:=k*diff(v(x,t),x$2)=diff(v(x,t),t):
bc:={v(x,0)=20,v(0,t)=0,v(50,t)=0}:
sol:=pdsolve(pde,bc,numeric,time=t,range=0..50):
p1:=sol:-plot(t=0,numpoints=50,color=red):
p2:=sol:-plot(t=20,numpoints=50,color=blue):
p3:=sol:-plot(t=50,numpoints=50,color=red):
p4:=sol:-plot(t=150,numpoints=50,color=blue):
p5:=sol:-plot(t=300,numpoints=50,color=red):
plots[display]({p1,p2,p3,p4,p5});

I will put the two questions in another way:
I would like to insert the boundary conditions not as algebraic functions, but rather as array/matrix. It is possible?
I would like to result in not a procedure, but rather as array/matrix. It is possible?

Thank you for your help.

I have a function g(x,t), which is the numerical result of a PDE.

How to calculate the function f (t), defined by:

f:=t->int(g(x,t),x=a..b)

I tried to calculate that way, but that did not work.

Thanks for the help.

I have a PDE system, which has IBCs that involve the unknown functions of the system. This system describes the mechanical evolution of a material volume, where material boundaries vary (it is an open physical system with mass addition). This problem has an analytical solution, but I am looking for a numerical solution. I do not know how to solve this (actually, I do not know if that's possible). I made a few attempts and I did not succeed.

On the last attempt, pdsolve returned the following error message: "Error, (in pdsolve/numeric/process_PDEs) PDEs can only contain dependent variables with direct dependence on the independent variables of the problem, got {u(H(t), t)}".

PDE_SYS.mw  (I re-uploaded the file because there was an error)

Well, I'd like some help on that. Thank you.

Both the equation defining a PDE and its boundary conditions involve functions that are the result of the numerical resolution process of an ODE system.

The PDE solution is obtained. However, when I want to calculate the value of the solution at some point the following error message is displayed: "Error, (in solnproc) unable to compute solution for t>HFloat(1.8936825887327868e15): unable to store HFloat(undefined)+HFloat(undefined)*I when datatype=float[8]".

I tried to formulate the problem differently. However, the error appeared again.

Where am I going wrong?

I've attached the PDE.mw file to the conference. 

Thank you for your help.

 

Is it possible to solve numerically a PDE, where the IBC is a function resulting from the numerical resolution of an ODE?

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