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Mathematics of Computation

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Parallel methods for the numerical integration of ordinary differential equations


Authors: Willard L. Miranker and Werner Liniger
Journal: Math. Comp. 21 (1967), 303-320
MSC: Primary 65.61
DOI: https://doi.org/10.1090/S0025-5718-1967-0223106-8
MathSciNet review: 0223106
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Abstract: In this paper we derive a class of numerical integration formulas of a parallel type for ordinary differential equations. These formulas may be used simultaneously on a set of arithmetic processors to increase the integration speed. Conditions for the convergence of such formulas are formulated. Explicit examples for two and four processor cases are derived. Results of numerical experiments are given which show an effective improvement in computation speed.


References [Enhancements On Off] (What's this?)

  • [1] B. Dejon, Numerical Stability of Difference Methods with Matrix Coefficients, RZ 198, Dec. 15, 1965.
  • [2] C. W. Gear, Hybrid methods for initial value problems in ordinary differential equations, J. Soc. Indust. Appl. Math. Ser. B Numer. Anal. 2 (1965), 69–86. MR 0179490
  • [3] Peter Henrici, Error propagation for difference method, John Wiley and Sons, Inc., New York-London, 1963. MR 0154416
  • [4] Peter Henrici, Discrete variable methods in ordinary differential equations, John Wiley & Sons, Inc., New York-London, 1962. MR 0135729
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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1967-0223106-8
Article copyright: © Copyright 1967 American Mathematical Society