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Stiff ODE solvers: A review of current and coming attractions. (English) Zbl 0614.65078
This article (62 pages) gives a review of methods and software solvers that are currently in use for stiff ordinary differential equations. Further, it presents a set of 10 stiff problems which show the challenges to the software and the capabilities of the solvers.
After an introduction into the notion of stiffness and into related problems (stability, method of lines, differential-algebraic systems), Section 2 presents a survey of methods for stiff problems including some comments on their relative merits. Section 3 is a description of available software. It begins with the history of ODE-solvers based on backward differentiation formulas and describes mainly the codes LSODE, EPISODE and related ones. Other codes (Runge-Kutta, blended and composite multistep, extrapolation, second-derivative) are mentioned briefly. An interesting and important part of this review is Section 4, where a set of 10 stiff problems is given. These examples are fairly representative with respect to many features and include problems arising in partial differential equations. It is shown how they can be solved by LSODE and its variants.
Reviewer: E.Hairer

##### MSC:
 65L05 Numerical methods for initial value problems 65N40 Method of lines for boundary value problems involving PDEs 65M20 Method of lines for initial value and initial-boundary value problems involving PDEs 65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis 34A34 Nonlinear ordinary differential equations and systems, general theory
##### Software:
DASSL; EPISODE; GEARS; IMSL Numerical Libraries; Larkin; LSODE; nag; ODEPACK
Full Text:
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