[74] in mathematical software users group
Re: Favourite diffeq algorithms?
daemon@ATHENA.MIT.EDU (Reid M. Pinchback)
Mon Mar 29 16:20:26 1993
To: jphill@rle-vlsi.mit.edu
Cc: msug@MIT.EDU
In-Reply-To: Your message of Mon, 29 Mar 93 15:54:27 -0500.
Date: Mon, 29 Mar 93 16:19:55 EST
From: "Reid M. Pinchback" <reidmp@Athena.MIT.EDU>
! Date: Mon, 29 Mar 1993 15:54:27 -0500
! From: jphill@rle-vlsi.mit.edu
!
! >Date: Mon, 29 Mar 93 16:04:07 EST
! >From: "Reid M. Pinchback" <reidmp@Athena.MIT.EDU>
!
! >I've been working implementing diffeq algorithms in Maple other than
! >the rkf45 used in Maple's dsolve/numeric routine, primarily because
! >people here tend to throw problems at it that it can't cope with.
!
! What sort of other algorithms? And what sort of problems can't it cope
! with?
(I'm cc'ing this to the list before somebody else asks me the same
question... I should have mentioned this in the original posting)
The Runge-Kutta methods are members of a larger class of methods that
includes Euler's and Heun's algorithms... namely, single-step methods.
They tend to have the advantage of simplicity, maybe speed, and
sometimes accuracy, but not stability. There is another class of
methods that I don't understand as well as I would like, called
multistep methods, that tend to be tougher to implement but often are
more stable. As I understand it, they are derived from multiple-term
finite difference equations. If there are other classes of solution
methods, I'm not really aware of them, except perhaps for interpolation
methods (of which I've heard but know nothing).
By the way, I suppose I also should have emphasized that I'm only
trying to deal with initial value problems, not looking at dealing
with boundary value problems... nasty!
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Reid M. Pinchback
Faculty Liaison
Academic Computing Services, MIT
