Stiff ODE solvers: A review of current and coming attractions
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.
scientific article; zbMATH DE number 3994946
scientific article