Semi-Implicit Runge-Kutta Procedures with Error Estimates for the Numerical Integration of Stiff Systems of Ordinary Differential Equations

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Semi-Implicit Runge-Kutta Procedures with Error Estimates for the Numerical Integration of Stiff Systems of Ordinary Differential Equations

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Journal of the ACM (JACM) archive
Volume 23 , Issue 3 (July 1976) table of contents

Pages: 455 - 460

Year of Publication: 1976

ISSN:0004-5411

Author

J. R. Cash

Department of Mathematics, Imperial College of Science and Technology, Exhibition Road, London SW7 2RH, England

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 3, Downloads (12 Months): 49, Citation Count: 2

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ABSTRACT

A -stable, semi-implicit Runge-Kutta procedures requiring at most one Jacobian evaluation per time step are developed for the approximate numerical integration of stiff systems of ordinary differential equations. A simple procedure for estimating the local truncation error is described and, with the help of this estimate, efficient integration procedures are derived. The algorithms are illustrated by direct application to a particular example.

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	ROSENI3ROCK, H H. Some general implicit processes for the numerical solution of differential equations. Comput J 5 (1963), 329-330
	2	CALAUAN, D. NumencM solutmn of linear systems with widely separated t~me constants Proc. IEEE 55 (Nov 1967), 2016-2017.
	3	ALLEN, R H , AND POTTLE, C Stable integration methods for electromc circuit analysis with widely separated time constants Proc. Sixth Annual Allerton Conf. on Circuit and System Theory, T. Trmk and R T. Chmn, Eds., pp. 311-320
	4	HAINES, C implicit integration processes with error estimates for the numermal solution of differential equations. Comput. J. 12 (1969), 183-187.
	5	LAMBENT, J.D. Computatwnal Methods ~n Ordinary D~fferential Equatwns Wiley, New York, 1973.
	6	LINIGER, W , AND WILLOUGHBY, R. Efficmnt numerical integration of stiff systems of ordinary d~fferentlal equatmns. Res. Rep RC 1970, IBM Thomas J Watson Research Center, Yorktown Heights, N Y, 1967.
	7	BJUREL, G, DAHLQUIST, G , LINDBERG, B, LINDE, S , AND ODEN, L. Survey of stiff ordinary differential equations Comput. Sci. Rep NA 70 11, Dep of Information Processing, Royal Inst. of Technology, Stockholm, Sweden, 1970.

CITED BY 2

	T. D. Bui, Errata and Comments on a Paper by J. R. Cash, Journal of the ACM (JACM), v.24 n.4, p.623, Oct. 1977
	T. D. Bui, Some A-Stable and L-Stable Methods for the Numerical Integration of Stiff Ordinary Differential Equations, Journal of the ACM (JACM), v.26 n.3, p.483-493, july 1979