A Multistep Generalization of Runge-Kutta Methods With Four or Five Stages

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A Multistep Generalization of Runge-Kutta Methods With Four or Five Stages

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Journal of the ACM (JACM) archive
Volume 14 , Issue 1 (January 1967) table of contents

Pages: 84 - 99

Year of Publication: 1967

ISSN:0004-5411

Author

John C. Butcher

University of Auckland, Auckland, New Zealand and Stanford Linear Accelerator Center, Stanford, California

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 3, Downloads (12 Months): 39, Citation Count: 2

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ABSTRACT

To obtain high-order integration methods for ordinary differential equatic which combine to some extent the advantage of Runge-Kutta methods on one hand and line multistep methods on the other, the use of “modified multistep” or “hybrid” method has been proposed by various researchers. In this paper formulas are derived for method which use one extra intermediate point than in the previously published methods so that there are analogues of the fourth-order Runge-Kutta method. A five-stage method of order 7 is already given.

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	William B. Gragg , Hans J. Stetter, Generalized Multistep Predictor-Corrector Methods, Journal of the ACM (JACM), v.11 n.2, p.188-209, April 1964 [doi>10.1145/321217.321223]
	2	J. C. Butcher, A Modified Multistep Method for the Numerical Integration of Ordinary Differential Equations, Journal of the ACM (JACM), v.12 n.1, p.124-135, Jan. 1965 [doi>10.1145/321250.321261]
	3	GEAI, C.W. Hybrid methods for initial value problems in ordimry differcatial equations. J. SIAM, hrum. Anal. {B}, 2 (1965), 69-86.
	4	DAHLOUmT, G. Convergence and stability in the numerical integration of ordinary differential eqmtions. Math. Scand. 4 (1956), 33-53.

CITED BY 2

	James Dyer, Generalized Multistep Methods in Satellite Orbit Computation, Journal of the ACM (JACM), v.15 n.4, p.712-719, Oct. 1968
	Phyllis Fox, A comparative study of computer programs for integrating differential equations, Communications of the ACM, v.15 n.11, p.941-948, Nov. 1972