Blended Linear Multistep Methods

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Blended Linear Multistep Methods

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 3 , Issue 4 (December 1977) table of contents

Pages: 326 - 345

Year of Publication: 1977

ISSN:0098-3500

Authors

Robert D. Skeel	Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana, IL
Antony K. Kong	Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana, IL

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 4, Downloads (12 Months): 37, Citation Count: 7

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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	BRAYTON, R.K., GUSTAVSON, F.G., AND HACHTEL, G.D. A new efficient algorithm for solving differential-algebraic systems using implicit backward differentiation formulas. Proc. IEEE 60 (1972), 98-108.
	2	Roy Leonard Brown, Jr., Multi-derivative numerical methods for the solution of stiff ordinary differential equations., 1975
	3	G. D. Byrne , A. C. Hindmarsh, A Polyalgorithm for the Numerical Solution of Ordinary Differential Equations, ACM Transactions on Mathematical Software (TOMS), v.1 n.1, p.71-96, March 1975 [doi>10.1145/355626.355636]
	4	ENBSC.HT, W.H. Studies in the numerical solution of stiff differential equations. Tech. Rep. 46, Dept. of Comptr. Sci., U. of Toronto, Toronto, Ont., Canada, Oct. 1972; also Ph.D. Th., Dept. of Comptr. Sci., U. of Toronto, 1972.
	5	ENPJGHT, W.H. Second derivative multistep methods for stiff ordinary differential equations. SIAM J. Numer. Anal. 11, 2 (Aprd 1974), 321-331.
	6	ENRIGHT, W.H. Optimal second derivative methods for stiff systems. In Stiff Differential Systems, R. A. Willoughby, Ed., Plenum Press, New York, 1974, pp. 95-111.
	7	ENRIGHT, W.H., HULL, T.E., AND LINDBERG, B. Comparing numerical methods for stiff systems of o.d.e.'s. BIT 15, 1 (1975), 10-48.
	8	FORSYTHE, G E., AND MOLER, C.B. Cor/tpuler 8olution of Linear Algebraic Systems. Prentice-Hall, Englewood Cliffs, N.J., 1967.
	9	C. W. Gear, Algorithm 407: DIFSUB for solution of ordinary differential equations [D2], Communications of the ACM, v.14 n.3, p.185-190, March 1971 [doi>10.1145/362566.362573]
	10	C. William Gear, Numerical Initial Value Problems in Ordinary Differential Equations, Prentice Hall PTR, Upper Saddle River, NJ, 1971
	11	HENRICI, P. Discrete Variable Methods in Ordinary Differential Equations. Wiley, New York, 1962.
	12	HINDMARSIt, A.C. GEAR: Ordinary differential equation solver. UCID-3001, Rev. 3, Lawrence Livermore Lab., U. of California, Livermore, Calif., 1974.
	13	Donald E. Knuth, The art of computer programming, volume 1 (3rd ed.): fundamental algorithms, Addison Wesley Longman Publishing Co., Inc., Redwood City, CA, 1997
	14	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 [doi>10.1145/321784.321786]
	15	LAMBERT, J.D. Linear multistep methods with mildly varying coefficients. Math. Comp. 24 (1970), 81-94.
	16	LAMBERT, J.D., AND SIGURDSSON, S.T. Multistep methods with variable matrix coefficients. SIAM J. Numer. Anal 9, 4 (Dec. 1972), 715-733.
	17	OSBORNS, M.R. On Nordsieck's method for the numerical solution of ordinary differential equations. BIT 6, I (1966), 52-57.
	18	S~A~PINE, L.F., ANY GORDON, M.K. Computer Solution of Ordinary Dijfferential Equations: Initial Value Problems. Freeman, San Francisco, Calif., 1975.
	19	M. K. Gordon , L. F. Shampine, Typical problems for stiff differential equations, ACM SIGNUM Newsletter, v.10 n.2-3, p.41-41, November 1975 [doi>10.1145/1053197.1053201]
	20	SKEEL, R.D. Equivalent forms of multistep formulas. Tech. Rep., Dept. of Comptr. Sci., U. of Illinois, Urbana, Ill., in preparation.
	21	SKEEL, R.D., AND KONG, A.K. Blended linear multistep methods. UIUCDCS-R-76-800, U. of Illinois, Urbana, Ill., June 1976.
	22	STETTSR, H.J. Analysis of Discretization Methods for Ordinary Differential Equations. Springer-Verlag, New York, 1973.

CITED BY 7

	Patrick W. Gaffney, A Performance Evaluation of Some FORTRAN Subroutines for the Solution of Stiff Oscillatory Ordinary Differential Equations, ACM Transactions on Mathematical Software (TOMS), v.10 n.1, p.58-72, March 1984
	Robert D. Skeel , Thu V. Vu, Note on blended linear multistep formulas, ACM Transactions on Mathematical Software (TOMS), v.12 n.3, p.223-224, Sept. 1986
	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
	R. Sacks-Davis, Fixed Leading Coefficient Implementation of SD-Formulas for Stiff ODEs, ACM Transactions on Mathematical Software (TOMS), v.6 n.4, p.540-562, Dec. 1980
	Luigi Brugnano , Cecilia Magherini, Blended implementation of block implicit methods for ODEs, Applied Numerical Mathematics, v.42 n.1, p.29-45, August 2002
	W. H. Enright , M. S. Kamel, Automatic Partitioning of Stiff Systems and Exploiting the Resulting Structure, ACM Transactions on Mathematical Software (TOMS), v.5 n.4, p.374-385, Dec. 1979
	M. Berzins , R. W. Brankin , I. Gladwell, The stiff integrators in the NAG library, ACM SIGNUM Newsletter, v.23 n.2, p.16-23, April 1988