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A review of recent developments in solving ODEs. (English) Zbl 0576.65071
This article gives a survey on the available software for the numerical solution of ordinary differential equations (initial value problems). The following methods are briefly explained and many references concerning their implementation are given: a) for non-stiff problems: explicit Runge-Kutta methods, multistep methods (Adams formulas), extrapolation methods based on the explicit mid-point rule, Taylor series methods, multirate methods; b) for stiff problems: linear multistep methods (BDF), implicit Runge-Kutta formulas, Rosenbrock methods, extrapolation methods, second-derivative methods, blended linear multistep methods, composite and cyclic multistep formulas. Finally, the literature for some special problems (implicit differential equations, differential-algebraic equations, discontinuities, high-frequency solutions) is discussed.
Reviewer: E.Hairer

MSC:
65L05 Numerical methods for initial value problems
65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis
34-04 Software, source code, etc. for problems pertaining to ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems, general theory
Software:
DASSL; DIFSUB; GEARBI; LSODE
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