Solution of Ordinary Differential Equations Using Two ``Off-Step'' Points

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Solution of Ordinary Differential Equations Using Two ``Off-Step'' Points

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Journal of the ACM (JACM) archive
Volume 14 , Issue 4 (October 1967) table of contents

Pages: 769 - 784

Year of Publication: 1967

ISSN:0004-5411

Authors

D. G. Brush	United Technology Center, Sunnyvale, California
J. J. Kohfeld	United Technology Center, Sunnyvale, California
G. T. Thompson	United Technology Center, Sunnyvale, California

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 3, Downloads (12 Months): 21, Citation Count: 0

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ABSTRACT

In a previous paper the authors suggested that the accurate correctors proposed by Gragg and Stetter for solving ordinary differential equations should be accompanied by similar predictors. In each method in that paper the corrector and one of the predictors use one “nonstop” point within the interval of integration. In the present paper a corrector is dealt with in which two “nonstep” points are used, and in which, to some degree, the authors have “balanced” the contributions of the errors in the predictors to the total local truncation error, a technique due to Butcher.

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	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]
	2	P. E. Chase, Stability Properties of Predictor-Corrector Methods for Ordinary Differential Equations, Journal of the ACM (JACM), v.9 n.4, p.457-468, Oct. 1962 [doi>10.1145/321138.321143]
	3	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]
	4	Richard W Hamming, Numerical methods for scientists and engineers (2nd ed.), Dover Publications, Inc., New York, NY, 1986
	5	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 [doi>10.1145/321371.321383]
	6	W. E. Milne , R. R. Reynolds, Stability of a Numerical Solution of Differential Equations, Journal of the ACM (JACM), v.6 n.2, p.196-203, April 1959 [doi>10.1145/320964.320976]
	7	W. E. Milne , R. R. Reynolds, Stability of a Numerical Solution of Differential Equations—Part II, Journal of the ACM (JACM), v.7 n.1, p.46-56, Jan. 1960 [doi>10.1145/321008.321014]
	8	NIXON, F .E . Principles of Automatic Controls. Prentice-Hall, Englewood Cliffs, N.J., 1953.
	9	NORDSIECK, A. On numerical integration of ordinary differential equations. Math. Comput. 16, 77 (1962), 22-49.