Additive methods for the numerical solution of ordinary differential equations

Authors:
G. J. Cooper and A. Sayfy

Journal:
Math. Comp. **35** (1980), 1159-1172

MSC:
Primary 65L05

MathSciNet review:
583492

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Abstract: Consider a system of differential equations . Most methods for the numerical solution of such a system may be characterized by a pair of matrices (*A, B*) and make no special use of any structure inherent in the system. In this article, methods which are characterized by a triple of matrices are considered. These methods are applied in an additive fashion to a decomposition and some methods have pronounced advantages when one term of the decomposition is linear. This article obtains algebraic conditions which give the order of convergence of such methods. Some simple examples are displayed.

**[1]**J. C. Butcher,*On the convergence of numerical solutions to ordinary differential equations*, Math. Comp.**20**(1966), 1–10. MR**0189251**, 10.1090/S0025-5718-1966-0189251-X**[2]**G. J. Cooper,*The order of convergence of general linear methods for ordinary differential equations*, SIAM J. Numer. Anal.**15**(1978), no. 4, 643–661. MR**0501920****[3]**J. Douglas Lawson,*Generalized Runge-Kutta processes for stable systems with large Lipschitz constants*, SIAM J. Numer. Anal.**4**(1967), 372–380. MR**0221759****[4]**Robert Skeel,*Analysis of fixed-stepsize methods*, SIAM J. Numer. Anal.**13**(1976), no. 5, 664–685. MR**0428717**

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DOI:
http://dx.doi.org/10.1090/S0025-5718-1980-0583492-2

Article copyright:
© Copyright 1980
American Mathematical Society