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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Error estimates for a stiff differential equation procedure
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by R. Sacks-Davis PDF
Math. Comp. 31 (1977), 939-953 Request permission

Abstract:

For numerical procedures which solve stiff systems of ordinary differential equations there are problems associated with estimating the local error. In this paper an analysis based on the linear model $y\prime = Ay$ is carried out for a particular method based on second derivative formulas. It is shown that there exists an error estimate based on a comparison between predicted and corrected values which is both reliable and efficient.
References
    W. H. ENRIGHT, Studies in the Numerical Solution of Stiff Ordinary Differential Equations, Tech. Report No. 46, Dept. of Computer Science, University of Toronto, 1972.
  • T. E. Hull, The numerical integration of ordinary differential equations. (With discussion.), Information Processing 68 (Proc. IFIP Congress, Edinburgh, 1968) North-Holland, Amsterdam, 1969, pp. 40–53. MR 0263245
  • T. E. Hull, The effectiveness of numerical methods for ordinary differential equations, Studies in Numerical Analysis, 2: Numerical Solutions of Nonlinear Problems (Symposia, SIAM, Philadelphia, Pa., 1968) Soc. Indust. Appl. Math., Philadelphia, Pa., 1970, pp. 114–121. MR 0267769
  • R. Sacks-Davis, Solution of stiff ordinary differential equations by a second derivative method, SIAM J. Numer. Anal. 14 (1977), no. 6, 1088–1100. MR 471323, DOI 10.1137/0714075
    • A. SEDGWICK, An Efficient Variable Order Variable Step Adams Method, Tech. Report No. 53, Dept. of Computer Science, University of Toronto, 1973.
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Additional Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Math. Comp. 31 (1977), 939-953
  • MSC: Primary 65L05
  • DOI: https://doi.org/10.1090/S0025-5718-1977-0474834-7
  • MathSciNet review: 0474834