A Modified Multistep Method for the Numerical Integration of Ordinary Differential Equations

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A Modified Multistep Method for the Numerical Integration of Ordinary Differential Equations

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Journal of the ACM (JACM) archive
Volume 12 , Issue 1 (January 1965) table of contents

Pages: 124 - 135

Year of Publication: 1965

ISSN:0004-5411

Author

J. C. Butcher

Stanford Linear Aecelerator Center, Stanford, California and University of Canterbury, Christchurch, New Zealand

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 1, Downloads (12 Months): 52, Citation Count: 10

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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	D&LQUIST, G. Convergence and stability in the numerical integration of ordiaar differential equations. Math. Stand. 4 (1956), 33-53.
	2	HENRICI, P. Discrete Variable Methods in Ordinary Differential Equations. Wiley, Nel York, 1962.
	3	KopAl, Z. Numarical Angly.'is, Chapman & lIall, London, 1955.
	4	Kvrrn, W. Bcitrag zur ihherungsweise Integration totaler Differentialgleicaugez Zeit. Math, Phys. 46 (1901), 435-453.
	5	NSTRDM, E. J. ubel' die mimerisctic Iiitegratin yon DiFFerenialgleichungen, Atta Soc. Sc. Pennicae 50, 13 (1925), 55 pp.
	6	MN W. E. Nurericat Solution oF Differential Equations. Wiley, New York, 1953.
	7	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]

CITED BY 10

	J. J. Kohfeld , G. T. Thompson, Multistep Methods With Modified Predictors and Correctors, Journal of the ACM (JACM), v.14 n.1, p.155-166, Jan. 1967
	D. G. Brush , J. J. Kohfeld , G. T. Thompson, Solution of Ordinary Differential Equations Using Two ``Off-Step'' Points, Journal of the ACM (JACM), v.14 n.4, p.769-784, Oct. 1967
	William B. Gruttke, Pseudo-Runge-Kutta Methods of the Fifth Order, Journal of the ACM (JACM), v.17 n.4, p.613-628, Oct. 1970
	James Dyer, Generalized Multistep Methods in Satellite Orbit Computation, Journal of the ACM (JACM), v.15 n.4, p.712-719, Oct. 1968
	Eldon Hansen, Cyclic composite multistep predictor-corrector methods, Proceedings of the 1969 24th national conference, p.135-139, August 26-28, 1969
	John C. Butcher, A Multistep Generalization of Runge-Kutta Methods With Four or Five Stages, Journal of the ACM (JACM), v.14 n.1, p.84-99, Jan. 1967
	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
	J. J. Kohfeld , G. T. Thompson, A Modification of Nordsieck's Method Using an ``Off-Step'' Point, Journal of the ACM (JACM), v.15 n.3, p.390-401, July 1968
	John Waters, Methods of numerical integration applied to a system having trivial function evaluations, Communications of the ACM, v.9 n.4, p.293-296, April 1966
	Truong Nguyen-Ba , Philip W. Sharp , Rémi Vaillancourt, Hermite-Birkhoff-Obrechkoff four-stage four-step ODE solver of order 14 with quantized step size, Journal of Computational and Applied Mathematics, v.222 n.2, p.608-621, December, 2008