MaplePrimes - answers and comments on Question, Numerical solution of nonlinear differential equation

T(x) in the boundary condition?

rlopez — Mon, 10 Sep 2012 22:15:34 Z

I suspect that Maple is complaining about T(x) appearing in the boundary condition.

RJL Maplesoft

@Noreen cute Thanks for the comment. I

sipeiw — Mon, 10 Sep 2012 23:37:55 Z

Thanks for the comment.

I understand the problem now. The boundary condition is for a constant heat flux from the surroundings to a colder surface. Do you have any suggestions on how to modify the T(x) in the boundary condition?

Robin boundary condition?

rlopez — Tue, 11 Sep 2012 01:34:58 Z

When the boundary condition is a linear combination of the heat flux and the temperature at an endpoint, I believe it is called a Robin boundary condition. (If the heat flux is prescribed, it is a Neumann condition. If the temperature is prescribed, it is a Dirichlet condition.)

At the left end, the condition could be expressed as D(T)(0)=a+b*T(0), for appropriate values of a and b.

RJL Maplesoft

agree

Noreen cute — Tue, 11 Sep 2012 22:28:56 Z

@sipeiw
plz follow Mr. rlopez, he guess it in right direction...

How to use dsolve comand when we have Robin bounda...

fernandonobrega — Wed, 19 Feb 2014 00:20:15 Z

@rlopez How to use dsolve comand when we have Robin boundary conditions?

Example

rlopez — Wed, 19 Feb 2014 14:35:34 Z

@fernandonobrega

Keeping the same ODE, I tried solving the BVP consisting of that equation and the two Robin conditions

BC:=D(T)(0)=1+3*T(0), D(T)(.2)=5+T(.2)

The command Q:=dsolve({ode,BC},T(x),numeric) succeeded, and the command Plots:-odeplot(Q) drew a graph of the solution of the BVP I had created.

Please try following this example and let us know if the problem you want to solve yields to these ideas.