A Class of Implicit Runge-Kutta Methods for the Numerical Integration of Stiff Ordinary Differential Equations

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A Class of Implicit Runge-Kutta Methods for the Numerical Integration of Stiff Ordinary Differential Equations

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Journal of the ACM (JACM) archive
Volume 22 , Issue 4 (October 1975) table of contents

Pages: 504 - 511

Year of Publication: 1975

ISSN:0004-5411

Author

J. R. Cash

Department of Mathematics, Imperial College, South Kensington, London S.W. 7, England

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 19, Downloads (12 Months): 174, Citation Count: 2

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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	ALLEN, R. H , AND POTTLE, C Stable integration methods for electronic circuit analysis with widely separated time constants Proc Sixth Annum Allerton Coal. on Circuit and System Theory, T Trick and RT Chmn, Eds , 1966, pp 311-320.
	2	BUTCHER, J. C Coefficients for the study of Runge-Kutta integration processes. J. Australian Math Soc. 3 (1963), 202-206
	3	BUTCHER, J C Implicit Runge-Kutta processes Math Comput 18 (1964), 50--64
	4	CALAHAN, D. A stable accurate method for the numerical integration of nonlinear systems Proc. IEEE 56 (April 1968), 744
	5	CURTIS, CF, AND HIRSCHFELDER, J.Integration of stiff equations. Proc. Nat. Acad. Sci U.S A 8 (1952), 235-243
	6	DAHLQUIST, G G A special stability problem for linear multistep methods BIT S (1963), 27--43
	7	EELE, B L. On PadE approximations to the exponential function and A-stable methods for the numerical solution of initial value problems. Res Rep CSRR 2010, Dep. of Applied Analysis and Computer Science, U of Waterloo, Waterloo, Ont, Canada, 1969.
	8	HAINES, C F Implicit integration processes with error estimates for the numerical solution of differential equations Computer J 15 (1968), 183-187
	9	LAMBENT, J D Compulatwnal Methods on Ordinary Differential Equations. Wiley, New York, 1973.
	10	LAPIDVS, L., aND SEINFELD, J. H. Numerical Solution of Ordinary Dfferenhal Equatwns. Academic Press, New York, 1971
	11	LINDBERG, B. On smoothing and extrapolation for the trapezoidal rule. Rep. Royal Inst. Technol , Stockholm, Sweden, Aug 1969
	12	ROSENBROCK, H H. Some general implicit processes for the numerical solution of differential equations. Computer J 5 (1963), 329-330

CITED BY 2

	Gopal K. Gupta , Ron Sacks-Davis , Peter E. Tescher, A review of recent developments in solving ODEs, ACM Computing Surveys (CSUR), v.17 n.1, p.5-47, March 1985
	G. Yu. Kulikov , S. K. Shindin, Adaptive nested implicit Runge--Kutta formulas of Gauss type, Applied Numerical Mathematics, v.59 n.3-4, p.707-722, March, 2009