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Error estimates for a stiff differential equation procedure

Author: R. Sacks-Davis
Journal: Math. Comp. 31 (1977), 939-953
MSC: Primary 65L05
MathSciNet review: 0474834
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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 [Enhancements On Off] (What's this?)

  • [1] 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.
  • [2] 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
  • [3] 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
  • [4] 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 0471323,
  • [5] 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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Article copyright: © Copyright 1977 American Mathematical Society

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