Re: NDSolve algorithm

*To*: mathgroup at christensen.cybernetics.net*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 castor.che.wisc.edu | > |University of Wisconsin-Madison | iasonas at cae.wisc.edu | > |Department of Chemical Engineering | Phone: (608) 262-7268 | > +-----------------------------------+--------------------------------------+ According to the Mathematica FAQ on the Web (http://www.wri.com/techsupport/)... :::::::::: 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