Comparing numerical methods for stiff systems of O.D.E:s |
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Authors: | W H Enright T E Hull B Lindberg |
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Institution: | 1. Department of Computer Science, University of Toronto, Toronto, Ontario, Canada
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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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