Parallel methods for the numerical integration of ordinary differential equations

Miranker, Willard L.; Liniger, Werner

doi:10.1090/S0025-5718-1967-0223106-8

Parallel methods for the numerical integration of ordinary differential equations
HTML articles powered by AMS MathViewer

by Willard L. Miranker and Werner Liniger PDF

Math. Comp. 21 (1967), 303-320 Request permission

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

Numerical Stability of Difference Methods with Matrix Coefficients

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 179490
Peter Henrici, Error propagation for difference method, John Wiley & Sons, Inc., New York-London, 1963. MR 0154416
Peter Henrici, Discrete variable methods in ordinary differential equations, John Wiley & Sons, Inc., New York-London, 1962. MR 0135729
Zdeněk Kopal, Numerical analysis. With emphasis on the application of numerical techniques to problems of infinitesimal calculus in single variable, John Wiley & Sons, Inc., New York, 1955. MR 0077213