Stiffness and Nonstiff Differential Equation Solvers, II: Detecting Stiffness with Runge-Kutta Methods

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Stiffness and Nonstiff Differential Equation Solvers, II: Detecting Stiffness with Runge-Kutta Methods

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 3 , Issue 1 (March 1977) table of contents

Pages: 44 - 53

Year of Publication: 1977

ISSN:0098-3500

Author

L. F. Shampine

Numerical Mathematics Division 5122, Sandia Laboratories, Albuquerque, NM

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 8, Downloads (12 Months): 77, Citation Count: 7

Additional Information:

references cited by index terms collaborative colleagues

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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	BJUREL, G., DAHLQUIST, G., LINDBERG, B., LINDE, S., AND ODIN, L. Survey of stiff ordinary differential equations. Rep. No. NA 70.11, Dep. Information Processing, Royal Inst. Technology, Stockholm, Sweden, 1970.
	2	HULL, T.E., ENRIGHT, W.H., FELLEN, B.M., AND SEDGWICK, A.E. Comparing numerical methods for ordinary differential equations./SIAM J. Numer. Anal. 9 (1972), 603-637.
	3	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]
	4	SHAMPINE, L.F. Stiffness and non-stiff differential equation solvers. In Numerische Behandlung yon Different~algleichungen, L. Collatz, Ed., Int. Series Numer. Math. 27, Birkhauser, Basel, Switzerland, 1975, pp. 287-301.
	5	SHAMPIN~, L.F. Limiting precision in differential equation solvers. Math. Comput. $8 (1974), 141-144.
	6	Lawrence F. Shampine , Richard C. Allen, Numerical Computing: An Introduction, Harcourt Brace College Publishers, 1973
	7	SHAMPINE, L.F., AND GORDON, M.K. Computer Solution of Ordinary Differential Equations: The Initial Value Problem. W. H. Freeman, San Francisco, Calif., 1975.
	8	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]
	9	SHAMPINE, L.F., WATTS, H.A., AND DAVENPORT, S.M. Solving non-stiff ordinary differential equations--the state of the art. SIAM Rev. 18 (1976), 376-411.

CITED BY 7

	M. S. Kamel , W. H. Enright , K. S. Ma, ODEXPERT: an expert system to select numerical solvers for initial value ODE systems, ACM Transactions on Mathematical Software (TOMS), v.19 n.1, p.44-62, March 1993
	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
	Kersti Ekeland , Brynjulf Owren , Eivor Øines, Stiffness detection and estimation of dominant spectrum with explicit Runge-Kutta methods, ACM Transactions on Mathematical Software (TOMS), v.24 n.4, p.368-382, Dec. 1998
	L. F. Shampine, Implementation of Rosenbrock Methods, ACM Transactions on Mathematical Software (TOMS), v.8 n.2, p.93-113, June 1982
	George Hall, Equilibrium states of Runge Kutta schemes, ACM Transactions on Mathematical Software (TOMS), v.11 n.3, p.289-301, Sept. 1985
	Ian Gladwell, Initial Value Routines in the NAG Library, ACM Transactions on Mathematical Software (TOMS), v.5 n.4, p.386-400, Dec. 1979
	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

INDEX TERMS

Primary Classification:
G. Mathematics of Computing

Additional Classification:
G. Mathematics of Computing
G.1 NUMERICAL ANALYSIS
G.1.7 Ordinary Differential Equations
Subjects: Stiff equations

General Terms:
Algorithms, Design, Theory

Collaborative Colleagues:

L. F. Shampine: colleagues

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