A Stability Criterion for Numerical Integration

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A Stability Criterion for Numerical Integration

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Journal of the ACM (JACM) archive
Volume 6 , Issue 3 (July 1959) table of contents

Pages: 363 - 365

Year of Publication: 1959

ISSN:0004-5411

Author

Herbert S. Wilf

Nuclear Development Corporation of America, White Plains, New York

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 3, Downloads (12 Months): 25, Citation Count: 3

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ABSTRACT

A necessary and sufficient condition is given for the absolute stability of multipoint numerical integration formulas for differential equations. The condition is that a certain matrix of low order, whose elements are computable from the coefficients of the integration formula, be positive definite. Two simple examples are 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	J. ScHv~, ~ber Potenzreihen Die im Innern der Einheitskreises beschr~nkt sind. J. Reine Angew. Math. 157 (1916), 205-2~and I48 (1917), 122-145.
	2	H. S. W~ta,, Analytic Theory of Continued Fractions, p. 298. Van Nostrand & Co., New York, 1946.
	3	F. B. HX{.DEBRASD, Methods of Applied Mathematics, p. 51. Prentice Hall, New York, 1952.

CITED BY 3

	Abbas I. Abdel Karim, The stability of the fourth order Runge-Kutta method for the solution of systems of differential equations, Communications of the ACM, v.9 n.2, p.113-116, Feb. 1966
	George Emanuel, The Wilf Stability Criterion for Numerical Integration, Journal of the ACM (JACM), v.10 n.4, p.557-561, Oct. 1963
	Abbas I. Abdel Karim, A Theorem for the Stability of General Predictor-Corrector Methods for the Solution of Systems of Differential Equations, Journal of the ACM (JACM), v.15 n.4, p.706-711, Oct. 1968