Abstract
This paper describes a technique for comparing numerical methods that have been designed to solve stiff systems of ordinary differential equations. The basis of a fair comparison is discussed in detail. Measurements of cost and reliability are made over a collection of 25 carefully selected problems. The problems have been designed to show how certain major factors affect the performance of a method.
The technique is applied to five methods, of which three turn out to be quite good, including one based on backward differentiation formulas, another on second derivative formulas, and a third on extrapolation. However, each of the three has a weakness of its own, which can be identified with particular problem characteristics.
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This project was supported by the National Research Council of Canada. Earlier work on the project was also supported by the Defence Research Board of Canada.
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Enright, W.H., Hull, T.E. & Lindberg, B. Comparing numerical methods for stiff systems of O.D.E:s. BIT 15, 10–48 (1975). https://doi.org/10.1007/BF01932994
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DOI: https://doi.org/10.1007/BF01932994