Re: Algorithm used in NDSolve
- To: MathGroup at yoda.physics.unc.edu
- Subject: Re: Algorithm used in NDSolve
- From: keiper
- Date: Mon, 26 Jul 93 09:18:50 CDT
John Gear (rmaxg at euler.ma.rmit.oz.au) writes
> Does anyone know what algorithm is used in NDSolve?
> Is it Gear's method?
This question has come up so many times that I know the exact reference
without having to look it up: Course Notes of the 1992 Mathematica
Conferences: Numerical Computation in Mathematica, by Jerry B. Keiper
and David Withoff (available from Wolfram Research, Inc.), page 46:
Initial value problems can be classified as either ``stiff'' or
``non-stiff''. Stiff problems are distinguished from non-stiff
problems in that stiff problems have interacting components that
vary on widely different scales. NDSolve[ ] uses the Adams
predictor-corrector method to handle non-stiff problems, and
backward differentiation formulae (i.e., Gear's method) for
stiff problems. NDSolve[ ] automatically detects the existence
of stiffness and chooses the correct method. The whole process
is transparent to the user so that a novice does not even have
to understand what stiffness is or recognize the presence of it.
> What is the order of the method and can the order be varied?
The algorithm is state-of-the-art and automatically chooses the order
based on the local behavior of the function and the PrecisionGoal.
Jerry B. Keiper
keiper at wri.com
Wolfram Research, Inc.
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