Implementation of Rosenbrock Methods

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Implementation of Rosenbrock Methods

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 8 , Issue 2 (June 1982) table of contents

Pages: 93 - 113

Year of Publication: 1982

ISSN:0098-3500

Author

L. F. Shampine

Applied Mathematics Research Department, Sandia National Laboratories, Albuquerque, NM

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 10, Downloads (12 Months): 107, 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	ALEXANDER, R. Diagonally implicit Runge-Kutta methods for stiff O.D.E.'s Szam J. Numer. Anal 6 (1977), 1006-1021.
	2	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 [doi>10.1145/322139.322147]
	3	BuI, T.D., AND BUI, T.R. Numerical methods for extremely stiff systems of ordinary differential equations. Appl. Math Model. 3 (1979~, 355-358.
	4	J. C. Butcher, A Transformed implicit Runge-Kutta Method, Journal of the ACM (JACM), v.26 n.4, p.731-738, Oct. 1979 [doi>10.1145/322154.322163]
	5	BYRNE, G.D., HINDMARSH, A.C., JACKSON, K.R., AND BROWN, H G. A comparison of two ODE codes: GEAR and EPISODE. Co/np. and Chem. Eng. 1 (1977), 133-147.
	6	CLINE, A.K., MOLER, C.B., STEWART, G.W., AND WILKINSON, J H. An estimate for the condition of a matrix. SIAM J. Numer. Anal. 16 (1979), 368-375.
	7	DONGARRA, J.J., BUNCH, ~.R., MOLER, C.B., AND STEWART, G.W. LINPACK User's Guide. Society for Industrial and Apphed Mathematics, Philadelphia, 1979.
	8	ENRIGHT, W.H., HULL, T.E., AND LINDBERG, B. Comparing numerical methods for stiff systems of O.D.E.'s. BIT 15 (1975), 10-48.
	9	C. William Gear, Numerical Initial Value Problems in Ordinary Differential Equations, Prentice Hall PTR, Upper Saddle River, NJ, 1971
	10	HALL, G, AND WATT, J.M. Modern Numerical Methods for Ordmary Dtfferenttal Equattons Clarendon Press, Oxford, England, 1976.
	11	HOUBAK, N., AND THOMSEN, P G SPARKS a FORTRAN subroutine for the solution of large systems of stiff ODE's with sparse jacoblans. NI-79-02, Institute for Numerical Analysis, Tech. Umv. of Denmark, Lyngby, 1979.
	12	HULME, B L., AND DANIEL, S.L. COLODE a colocation subroutine for ordinary differential equations. SAND74-0380, Sandia National Laboratories, Albuquerque, N. Mex., 1974.
	13	KAPS, P., AND RENTROP, P Generalized Runge-Kutta methods of order four with stepsize control for stiff ordinary differential equations. Numer. Math 33 (1979), 55-68.
	14	KAPS, P, AND WANNER, G. A study of Rosenbrock-type methods of high order, lnstitut fur Mathematlk and Geometrie, Universitat innsbruck, Innsbruck, Austria, 1979.
	15	LAPIDUS, L., AND SCHIESSER, W.E. Numerwal Methods for D~fferential Systems. Academic, New York, 1976
	16	NAG CENTRAL OFFICE 7 Banbury Road, Oxford, England, NAG Manual, Mark 7, 1979.
	17	PROTHERO, A., AND ROBINSON, A. On the stability and accuracy of one-step methods for solving stiff systems of ordinary differential equations. Math Comp. 28 (1974), 145-162.
	18	RODRIGUES, A., AND BEIRA, E.C Staged approach of percolation processes. AIChE J. 25 (1979), 416-423
	19	L. F. Shampine, Stiffness and Nonstiff Differential Equation Solvers, II: Detecting Stiffness with Runge-Kutta Methods, ACM Transactions on Mathematical Software (TOMS), v.3 n.1, p.44-53, March 1977 [doi>10.1145/355719.355722]
	20	SHAMPINE, L.F. Implementation of imphclt formulas for the solution of O.D.E.'s. SIAM J. Sc~. Stat. Comp. 1 (1980), 103-118.
	21	SHAMPINE, L.F., AND WATTS, H.A. The art of writing a Runge-Kutta code, Part i. In Mathematwal Software Ill, J. R. Rice (Ed.). Academic, New York, 1977.
	22	SHAMPINE, L.F., AND WATTS, H.A. The art of writing a Runge-Kutta code, II. Appl. Math. Comp 5 (1979), 93-121.
	23	SHAMPINE, L.F., AND WATTS, H.A. DEPAC--Design of a user oriented package of ODE solvers. SAND79-2374, Sandia National Laboratories, Albuquerque, N. Mex., 1980.
	24	STOER, ~{., AND BULIRSCH, R. Introduction to Numerwal Analysts. Springer-Verlag, New York, 1980.
	25	UEBERHUBER, C.W Implementation of defect correction methods for stiff differential equations. Comput. 23 (1979), 205-232.
	26	VAN DER I'~OUVEN, P.J. Construction of Integration Formulas for Initial Value Problems North-Holland, Amsterdam, The Netherlands, 1977.
	27	VILLADSEN, J., AND MICHELSEN, M.L. Solutton of D~fferent~al Equation Models by Polynomial Approximation. Prentice-Hall, Englewood Cliffs, N.J., 1978.
	28	WILLOUGHBY, R.A. St~ffD~fferenttal Systems. Plenum Press, New York, 1974.
	29	WOLFBRANDT, A. A study of Rosenbrock processes with respect to order conditions and stiff stability. 77.01R, Dep. Computer Science, Univ. of Goteborg, Goteborg, Sweden, 1977.

CITED BY 2

	A. Ostermann , P. Kaps , T. D. Bui, The solution of a combustion problem with Rosenbrock methods, ACM Transactions on Mathematical Software (TOMS), v.12 n.4, p.354-361, Dec. 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