Modified Multistep Methods Based on a Nonpolynomial Interpolant

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Modified Multistep Methods Based on a Nonpolynomial Interpolant

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

Pages: 143 - 154

Year of Publication: 1967

ISSN:0004-5411

Author

Brian Shaw

Department of Computer Sciences, University of Texas, Austin, Texas and Institut für angewandte Mathematik, Eidgenossische Technische Hochschule, Zurich, Switzerland

Publisher

ACM New York, NY, USA

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ABSTRACT

A new class of multistep formulas with variable coefficients is derived for the numerical integration of the ordinary differential equation y′ = f(x, y) whose theoretical solution possesses a singularity. A first numerical solution is obtained along with estimates for the behavior of the singularity, and these estimates are then used to obtain further numerical solutions.

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	LAMBERT, J. D., AND SAW, B. A method for the numerical solution of y' = f(x, y) based on a self-adj usting non-polynomial interpolant. Math. Comp. 20 (1966), 11-20.
	2	-- AND -- A generalisation of multistep methods for ordinary differential equations. Num. Math. 8(1966), 250-263.
	3	SIMON, W.E. Numerical technique for solution and error estimate for the initial value problem. Math. Comp. 19 (1965), 387-393.
	4	HENKIVlc, P. Discrete Variable Methods in Ordinary Differential Equations. John Wiley and Sons, New York, 1962.
	5	HILDERMANND, F. B. Introduction to Numerical Analysis. McGraw-Hill Book Co., New York, 1956.
	6	NEWBERY, A. C.R. Multistep integration formulae. Math. Comp. 17 (1963), 452-455.