# Question:Problem with Boundary Conditions

## Question:Problem with Boundary Conditions

Maple

My coursemate and I tried to solve a differential equation using the following code:

>PDE := diff(Sigma(R, t), t) = 3*(diff(R^.5*(diff(Sigma(R, t)*R^.5, R)), R))/R;
>IBC := {Sigma(0, t) = 10, Sigma(R, 0) = 0};
>pds := pdsolve(PDE, IBC, numeric, Sigma(t, R), indepvars() = (R, t), time = t, range = 0 .. infinity)
%
Error, (in pdsolve/numeric/par_hyp) Incorrect number of boundary conditions, expected 2, got 1

As can be clearly seen, we have specified two boundary conditions, so what do we have to do to convince Maple that this is the case? Also, we have changed these boundary conditions because Maple didn't like the following:

> IBC := {Sigma(R, 0) = 0, Sigma(infinity, t) = 0};
> pds := pdsolve(PDE, IBC, numeric, Sigma(t, R), indepvars() = (R, t), time = t, range = 0 .. infinity);
%;
Error, (in pdsolve/numeric/process_IBCs) initial/boundary conditions must depend upon exactly one of the independent variables: Sigma(infinity, t) = 0

Since this error goes away when we stop using sigma=0 at R=infinity, I presume that the error is being caused by the use of infinity in the boundary conditions - unfortunately, we need to use infinity in the boundary conditions. How do we do this?

Our professor wants us to set sigma(R,0) equal to a Dirac delta function, but I have no idea how to even start going about doing that in Maple, so any help on that would also be appreciated.

Lastly, as can be seen in both of the snippets above, we are using indepvars, but we have had to put '()' after the keyword in order to get Maple to stop throwing up independent variable-related errors. Is this the proper fix, or is it a fudge that will cause problems later?

The error we get:

> pds := pdsolve(PDE, IBC, numeric, Sigma(t, R), indepvars = (R, t), time = t, range = 0 .. infinity);
%;
Error, (in pdsolve/numeric) invalid input: rhs received {indepvars = (R, t)}, which is not valid for its 1st argument, expr

Any help is gratefully appreciated. ﻿