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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
MathSciNet review: 1423077
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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: http://dx.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