Composition constants for raising the orders of unconventional schemes for ordinary differential equations

Authors:
William Kahan and Ren-Cang Li

Journal:
Math. Comp. **66** (1997), 1089-1099

MSC (1991):
Primary 34A50, 65L05

DOI:
https://doi.org/10.1090/S0025-5718-97-00873-9

MathSciNet review:
1423077

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Abstract | References | Similar Articles | Additional Information

Abstract: Many models of physical and chemical processes give rise to ordinary differential equations with special structural properties that go unexploited by general-purpose software designed to solve numerically a wide range of differential equations. If those properties are to be exploited fully for the sake of better numerical stability, accuracy and/or speed, the differential equations may have to be solved by unconventional methods. This short paper is to publish composition constants obtained by the authors to increase efficiency of a family of mostly unconventional methods, called *reflexive*.

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Additional Information

**William Kahan**

Affiliation:
Computer Science Division and Department of Mathematics, University of California at Berkeley, Berkeley, California 94720

Email:
wkahan@cs.berkeley.edu

**Ren-Cang Li**

Affiliation:
Mathematical Science Section, Oak Ridge National Laboratory, P.O. Box 2008, Bldg. 6012, Oak Ridge, Tennessee 37831-6367

Email:
na.rcli@na-net.ornl.gov

DOI:
https://doi.org/10.1090/S0025-5718-97-00873-9

Keywords:
Ordinary differential equations,
reflexive methods,
composition schemes,
palindromic schemes

Received by editor(s):
June 10, 1996

Additional Notes:
The first author was supported in part by the Office of Naval Research contract N00014-90-J-1372 and National Science Foundation contract ASC-9005933.

The second author was supported in part by a Householder Fellowship in Scientific Computing at Oak Ridge National Laboratory, supported by the Applied Mathematical Sciences Research Program, Office of Energy Research, United States Department of Energy contract DE-AC05-96OR22464 with Lockheed Martin Energy Research Corporation.

Article copyright:
© Copyright 1997
American Mathematical Society