Improving the Efficiency of Matrix Operations in the Numerical Solution of Stiff Ordinary Differential Equations

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Improving the Efficiency of Matrix Operations in the Numerical Solution of Stiff Ordinary Differential Equations

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 4 , Issue 2 (June 1978) table of contents

Pages: 127 - 136

Year of Publication: 1978

ISSN:0098-3500

Author

W. H. Enright

Department of Computer Science, University of Toronto, Toronto, Ont., Canada

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 1, Downloads (12 Months): 28, Citation Count: 5

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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	ALEXANDER, R.K. Semi-implicit RK methods for stiff ODE's. Presented at SIAM Nat. Meeting, Chicago, Ill., 1976.
	2	BLUE, J.L., AND GUMMEL, H.K. Rational approximation to matrix exponential for systems of stiff differential equations. J. Comput. Physics 5 (1969), 70-83.
	3	BRowN, R L Multi-derivative numerical methods for the solution of stiff ordinary differential equations. Teeh. Rep. UIUCDCS-R-74-672, Dept. Comptr. Sei., U. of Illinois at Urbana-Champaign, Urbana, Ill., 1975.
	4	BUTCHER, J'.C. Implicit Runge-Kutta processes. Math. Comput. 18 (1964), 50-64.
	5	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]
	6	B~RNE, G.D., AND I-IINDMARSH, A.C. EPISODE: An experimental package for the integration of systems of ordinary differential equations. Rep. UCID-30112, Lawrence Livermore Lab., Livermore, Calif., 1975.
	7	CROVZEIX, M. Sur l'approximation des e~quations diff~rentielles operationnelles lin4aires par des mdthodes de Runge Kutta. Ph.D. Diss., U. of Paris, 1975.
	8	DAVlSON, E.J. An algorithm for the computer simulation of very large dynamic systems. Automatica 9 (1973), 665-675.
	9	ENRmRT, W.H. Second derivative multistep methods for stiff ordinary differential equations. SIAM J. Numer. Anal. 11 (1974), 321-331.
	10	ENRIGHT, W.H. Optimal second derivative methods for stiff systems. In Stiff Differential Systems, R.A. Willoughby, Ed., Plenum Press, New York, (1974), 95-111.
	11	ENRIGHT, W.H., HULL, T.E., AND LINDBER6, B. Comparing numerical methods for stiff systems of O.D.E.'s. BIT 15 (1975), 10-48.
	12	FLETCHER, R. The quest for a natural metric. Presented at Syrup. on Matrix Methods in Optimization, Argonne Nat. Lab., Argonne, Ill., 1976.
	13	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]
	14	HINDMARSH, A.C. GEAR: Ordinary differential equation system solver. Rep. UCID- 30001, Rev. 3, Lawrence Livermore Lab., Livermore, Calif., 1974.
	15	LAWSON, J.D., AND EHLE, B.L. Improved generalized Runge-Kutta. Proc. Canadian Comptr. Conf., Session 72, 1972, pp. 223201-223213.
	16	MARTIN, R.S , AND WILKINSON, .I.H. Similarity reduction of a general matrix to Hessenberg form. (Handbook Series in Linear Algebra). Numer. Math. 12 (1968), 349-368.
	17	S~tlT~I, B.T., BOYLE, J.M., GARBOW, B.S., IKEBE, Y., KLEMA, V.C., AND MOLER, C.B. Matrix Eigensystem Routines--EISPACK Guide: Leclure Noles on Computer Science, 6. Springer-Verlag, New York, 1974.
	18	SMITH, I.M, SIEMUNItlCI~, J.L., AND GLADWELL, I. A comparison of old and new methods for large systems of ordinary differential equations arising from parabolic partial differential equations. Numer. Anal. Rep. 13, Dept. of Math, U. of Manchester, Manchester, England, 1975.
	19	J. H. Wilkinson, The algebraic eigenvalue problem, Oxford University Press, Inc., New York, NY, 1988

CITED BY 5

	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
	Lawrence F. Shampine, Evaluation of a Test Set for Stiff ODE Solvers, ACM Transactions on Mathematical Software (TOMS), v.7 n.4, p.409-420, Dec. 1981
	David S. Watkins , Ralph W. HansonSmith, The Numerical Solution of Separably Stiff Systems by Precise Partitioning, ACM Transactions on Mathematical Software (TOMS), v.9 n.3, p.293-301, Sept. 1983
	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
	Roger Alexander, Design and implementation of DIRK integrators for stiff systems, Applied Numerical Mathematics, v.46 n.1, p.1-17, July 2003