The Validation and Comparison of Programs for Stiff Systems
Software for solving stiff systems of ordinary differential equations should be easy to understand, reliable, efficient and convenient. Good structuring, the use of appropriate language conventions, and proofs of correctness contribute towards ease of understanding. Careful comparisons are needed to assess reliability and efficiency. Further testing and packaging help make the system convenient to use. Each of these topics is discussed, and comparisons between five different methods are presented. An adaptation of Gear’s backward difference method, the second-derivative method of Enright, and an extrapolation method based on ideas due to Dahlquist and Lindberg are reliable and reasonably efficient, although for each of these methods there is a class of problems for which the method is somewhat less efficient than the other two. On the other hand, an implicit Runge-Kutta method and a modification of the generalized Runge-Kutta method due to Ehle and Lawson did not compare favourably with the first three.
KeywordsExtrapolation Method Stiff System Calling Sequence Language Convention Stiff Ordinary Differential Equation
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