boundary value problem, to solve (13.10.95)

Ulrich Klein

We have a problem in solving a diﬀerential equation. We have a diﬀerential equation, say de and an initial value condition: $$y(0)=0$$ and a boundary value condition: D(y)(20)=0, eg.

If we try to solve this equation using the dsolve command, Maple complains about the second condition. Besides, we use the numeric option of the dsolve command.

Do you know a way to solve such an equation with Maple?

Maple’s numeric dsolve is, as the on-line help describes, of use only for initial value problems. You are asking for the numerical solution of a two-point boundary value problem.

While you do not provide enough information to know exactly what type of ODE you are attempting to solve, I might have something that will be of interest.

I have recently developed a Maple implementation of the simple shooting method.

This procedure works very much like dsolve[numeric]. It must be used with caution, as the numerical method is not always stable. A paper introducing this procedure (shoot) and demonstrating its usage on three problems will appear in the upcoming Special Issue of MapleTech. (These examples are nonlinear and some involve systems.)

The on-line help for shoot, which includes two (simple) examples, is attached to the end of this message.

Anyone interested in this paper and/or procedure should send mail to: Douglas B. Meade

SEE ALSO: dsolve[numeric], userinfo PS: It worked very well for our problem. U. Klein