Automatic Partitioning of Stiff Systems and Exploiting the Resulting Structure

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Automatic Partitioning of Stiff Systems and Exploiting the Resulting Structure

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 5 , Issue 4 (December 1979) table of contents

Pages: 374 - 385

Year of Publication: 1979

ISSN:0098-3500

Authors

W. H. Enright	Department of Computer Science, University of Toronto, Toronto, Ont., Canada M5S 1A7
M. S. Kamel	Department of Computer Science, University of Toronto, Toronto, Ont., Canada M5S 1A7

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 3, Downloads (12 Months): 22, Citation Count: 3

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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	ADDISION, C. Private communication, 1978.
	2	ALFELD, P., AND LAMBERT, J.D. Correction in the dominant space: A numerical technique for a certain class of stiff initial value problems. Math. Comput. 11, 140 (1977), 922-938.
	3	BEDET, R.A., ENRIGHT, W.H., AND HULL, T.E. STIFF DETEST: A program for comparing numerical methods for stiff ordinary differential equations. Tech. Rep. No. 81, Dept. of Comptr. Sci., U. of Toronto, Toronto, Canada, 1975.
	4	BRANIN, F.H. Computer methods of network analysis. Proc. IEEE 55, 11 (Nov. 1967), 1787-1801.
	5	DAHLQUIST, G. A numerical method for some ordinary differential equations with large Lipschitz constants. In Informatzon Processing 68, A. Morell, Ed., North-Holland Pub. Co., Amsterdam, 1969, pp. 183-186.
	6	DAHLQUIST, G. Problems related to the numerical treatment of stiff differential equations. Proc Int. Comptg. Symp. 1973, A. Gunther et al., Eds., North-Holland Pub. Co, Amsterdam, 1974, pp. 307-314.
	7	DAHLQUIST, G. Recent work on stiff differential equations. Rep. TRITA-NA-7512, Dept. of Inform Processing, Royal Inst. of Technology, Stockholm, Sweden, 1975.
	8	DAHLQUIST, G. Error analysis for a class of methods for still nonlinear initial value problems. Proc. Numerical Analysm Conf., Dundee, Scotland, 1975, Springer Lecture Notes in Math., No. 506, Springer, New York, pp. 60-74.
	9	DAVlSON, E.J. An algorithm for the computer snnulation of very large dynamic systems. Automatica 9 (1973), 665-675.
	10	ENRIGHT, W.H. Optimal second derivative methods for stiff systems. In SttffD,fferenttal Systems, R. Willoughby, Ed., Plenum Press, New York, 1974, pp. 95-111.
	11	W. H. Enright, Improving the Efficiency of Matrix Operations in the Numerical Solution of Stiff Ordinary Differential Equations, ACM Transactions on Mathematical Software (TOMS), v.4 n.2, p.127-136, June 1978 [doi>10.1145/355780.355784]
	12	ENRIGHT, W.H., HULL, T.E., AND LINDBERG, B. Companng numerical methods for stiff systems of ODE's. BIT 15 (1975), 10-48.
	13	FINDEN, W.F Some numerical procedures for solving systems of ODE's containing a small parameter. Res. Rep. CS-75-22, Dept. of Comptr. Scl., U. of Waterloo, Waterloo, Canada, 1975.
	14	HINDMARSH, A.C. The LLL family of ordinary differential equations solvers. Rep. UCRL-78129, Lawrence Livermore Lab., U. of California, Livermore, Calif., 1976
	15	HINDMARSH, A.C., AND BYRNE, G D. EPISODE" An experimental package for the integration of systems of ordinary chfferentlal equations. Rep. UCID-30112, Lawrence Livermore Lab., U. of California, Livermore, Calif., 1975.
	16	HOFFER, E. Partially nupliclt method for large stiff system of ODE's with only few equations introducing small time constants. SIAM J. Numer. Anal. 13, 5 (1976), 645-663.
	17	LAWSON, C.L., AND HANSON, R.J. Solwng Least Squares Problems. Prentice-Hall, Englewood Cliffs, N.J, 1974.
	18	LEE, H.B. Matrix filtermg as an aid to numencal integration. Proc. IEEE 55, 11 (Nov. 1967), 1826-1831.
	19	MACMILLAN, D.B. Asymptotm methods for systems of differential equations in which some variables have very short response times. SIAM J. Appl. Math. 16, 4 (1968), 704-721.
	20	MmANKER, W.L. Numerical methods of boundary layer type for stiff systems of differential equations. Computing, 11 (1973), 221-234.
	21	ODEN, L. An experimental and theoretmal analysis of the SAPS method for stiff ordinary differential equatmns. Rep. NA 71.28, Dept. of Inform. Processing, Royal Inst. of Technology, Stockholm, Sweden, 1971.
	22	ROBERTSON, H.H. Numermal integratmn of systems of stiff ordinary differential equations with specml structure. J Inst. Math. Appl. 18, 2 {1976), 249-263.
	23	Robert D. Skeel , Antony K. Kong, Blended Linear Multistep Methods, ACM Transactions on Mathematical Software (TOMS), v.3 n.4, p.326-345, Dec. 1977 [doi>10.1145/355759.355762]

CITED BY 3

	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
	Rafik Djouad , Bruno Sportisse, Partitioning techniques and lumping computation for reducing chemical kinetics: APLA: an automatic partitioning and lumping algorithm, Applied Numerical Mathematics, v.43 n.4, p.383-398, December 2002
	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