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Re: NDSolve algorithm

  • To: mathgroup at
  • Subject: [mg1648] Re: [mg1604] NDSolve algorithm
  • From: John Fultz <jfultz>
  • Date: Sat, 8 Jul 1995 04:55:33 -0400

> What kind of algorithm does NDSolve use?
> -- 
> +-----------------------------------+--------------------------------------+
> |Iasson G. Mustakis                 | Email: iasonas at   |
> |University of Wisconsin-Madison    |        iasonas at          |
> |Department of Chemical Engineering | Phone:  (608) 262-7268               |
> +-----------------------------------+--------------------------------------+ 

According to the Mathematica FAQ on the Web (


NDSolve uses an Adams Predictor-Corrector method for non-stiff
differential equations and backward difference formulas (Gear method)
for stiff differential equations. It switches between the two methods
using heuristics based on the adaptively selected step size. It starts
with the non-stiff method under essentially all conditions, and checks
for the advisability of switching methods every 10 or 20 steps.

The algorithms and the heuristics for switching between algorithms are
described in the following references:

     Alan C. Hindmarsh, "ODEPACK: A Systematized Collection of ODE
     Solvers", in Scientific Computing, R. S. Stepleman et. al. (eds).
     North-Holland, Amsterdam (1983), pp. 55-64.

     Linda R. Petzold, "Automatic Selection of Methods for Solving
     Stiff and Nonstiff Systems of Ordinary Differential Equations",
     SIAM Journal of Scientific and Statistical Computing, 4 (1983),
     pp. 136-148.


John Fultz
Technical Support

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