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.