Predictor-Corrector Methods of High Order With Improved Stability Characteristics

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Predictor-Corrector Methods of High Order With Improved Stability Characteristics

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Journal of the ACM (JACM) archive
Volume 13 , Issue 3 (July 1966) table of contents

Pages: 374 - 385

Year of Publication: 1966

ISSN:0004-5411

Author

Fred T. Krogh

TRW Systems Group, Redondo Beach, California

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 1, Downloads (12 Months): 34, Citation Count: 3

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ABSTRACT

Some new predictors are presented for use with the Adams-Moulton correctors of orders 4 through 8. The resulting algorithms have better stability characteristics than the usual ones which employ the Adams Bashforth predictors and at the same time require no additional storage. The regions of absolute and relative stability for the methods mentioned above and for the iterated Adams-Moulton correctors are given. Results obtained using the various methods are compared.

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	T. E. Hull , A. L. Creemer, Efficiency of Predictor-Corrector Procedures, Journal of the ACM (JACM), v.10 n.3, p.291-301, July 1963 [doi>10.1145/321172.321176]
	2	RALSTON, ANTtmNY. Relative stability in the numerical solution of ordinary differential equations. SIAM Rev. 7 (1965), 114--125.
	3	BaOWN, ROBERT ., RILEY, JAMES D., AND BENNETT, MORRIS M. Stability properties of hdams-Moulton type methods. Math. of Comput. 19 (1965), 90-96.
	4	R. L. Crane , R. W. Klopfenstein, A Predictor-Corrector Algorithm with an Increased Range of Absolute Stability, Journal of the ACM (JACM), v.12 n.2, p.227-241, April 1965 [doi>10.1145/321264.321272]
	5	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]

CITED BY 3

	Fred T. Krogh, A Test for Instability in the Numerical Solution of Ordinary Differential Equations, Journal of the ACM (JACM), v.14 n.2, p.351-354, April 1967
	Fred T. Krogh, On Testing a Subroutine for the Numerical Integration of Ordinary Differential Equations, Journal of the ACM (JACM), v.20 n.4, p.545-562, Oct. 1973
	Zahari Zlatev , Per Grove Thomsen, Automatic Solution of Differential Equations Based on the User of Linear Multistep Methods, ACM Transactions on Mathematical Software (TOMS), v.5 n.4, p.401-414, Dec. 1979