Quality of Runge--Kutta formulas
Critical evaluation of mathematical software is essential for the designation of items worthy of general acceptance and for the production of improved software. In the case of codes to solve the initial-value problem for ordinary differential equations, the usual procedure is to compare performance on a set of test problems. The value of such comparisons hinges on the hypothesis that the performance in nearly all respects depends only on the behavior of the solutions, not the form of the equations themselves. Unfortunately, this is not realistic for codes based on Runge--Kutta methods. Confronted with the fact that changing the form of an equation without altering its solution can reverse the relative efficiency of two Runge--Kutta formulas, how can one decide which formula to use. Relative behavior is predicted ''on the average'' and applied to assessing the quality of Runge--Kutta formulas and their error estimators. This conceptual tool and other aspects of quality illustrated in the generation of new formulas of high quality. 3 figures, 2 tables.
- Research Organization:
- Sandia Labs., Albuquerque, N.Mex. (USA)
- DOE Contract Number:
- AT(29-1)-789
- OSTI ID:
- 7266444
- Report Number(s):
- SAND-76-0370
- Country of Publication:
- United States
- Language:
- English
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