Composition constants for raising the orders of unconventional schemes for ordinary differential equations
Authors:
William Kahan and RenCang Li
Journal:
Math. Comp. 66 (1997), 10891099
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 generalpurpose 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
RenCang Li
Affiliation:
Mathematical Science Section, Oak Ridge National Laboratory, P.O. Box 2008, Bldg. 6012, Oak Ridge, Tennessee 378316367
Email:
na.rcli@nanet.ornl.gov
DOI:
http://dx.doi.org/10.1090/S0025571897008739
PII:
S 00255718(97)008739
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 N0001490J1372 and National Science Foundation contract ASC9005933.
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 DEAC0596OR22464 with Lockheed Martin Energy Research Corporation.
Article copyright:
© Copyright 1997
American Mathematical Society
