Control theoretic techniques for stepsize selection in explicit Runge-Kutta methods

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Control theoretic techniques for stepsize selection in explicit Runge-Kutta methods

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 17 , Issue 4 (December 1991) table of contents

Pages: 533 - 554

Year of Publication: 1991

ISSN:0098-3500

Author

Kjell Gustafsson

Department of Automatic Control, Lund Institute of Technology, P.O. Box 118, S-221 00 Lund, Sweden

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 6, Downloads (12 Months): 62, Citation Count: 12

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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	Karl J. Åström , Björn Wittenmark, Computer-controlled systems: theory and design (2nd ed.), Prentice-Hall, Inc., Upper Saddle River, NJ, 1990
	2	ENRIGHT, W. H. HULL, T. E., AND LINDBERG, B. Comparing numerical methods lor still systems of ODE's. BIT 15, 1 (1975), 28-33.
	3	Gene F. Franklin , David J. Powell , Abbas Emami-Naeini, Feedback Control of Dynamic Systems, Prentice Hall PTR, Upper Saddle River, NJ, 2001
	4	C. William Gear, Numerical Initial Value Problems in Ordinary Differential Equations, Prentice Hall PTR, Upper Saddle River, NJ, 1971
	5	Kjell Gustafsson , Michael Lundh , Gustaf Söderlind, A PI stepsize control for the numerical solution of ordinary differential equations, BIT, v.28 n.2, p.270-287, February 1988 [doi>10.1007/BF01934091]
	6	GUSTAFSSON, K. Stepmze control in ODE-solvers-analysis and synthesis Licentiate thems TFRT-3199, Dept. of Automatic Control, Lund Inst. of Technology, Lund, Sweden.
	7	HAINES, E. NCRSETT, S. P., AND WANNER, G Solvmg Ordtnary Dtfferent~al Equattons, I, NonsttffProblems. Springer-Verlag, New York, pp. 112, 132, 167, 171.
	8	George Hall, Equilibrium states of Runge Kutta schemes, ACM Transactions on Mathematical Software (TOMS), v.11 n.3, p.289-301, Sept. 1985 [doi>10.1145/214408.214424]
	9	George Hall, Equilibrium states of Runge-Kutta schemes: part II, ACM Transactions on Mathematical Software (TOMS), v.12 n.3, p.183-192, Sept. 1986 [doi>10.1145/7921.7922]
	10	HAbL, G., AND HmHAM, D. J. Analysis of stepsize selection for Runge-Kutta codes NA report 137, Univ of Manchester, 1987
	11	HIGHAM, D. J., AND HALL, G Embedded Runge-Kutta formulae with stable equilibrium states. NA report 140, Umv of Manchester, 1987.
	12	MOLER, C., LITTLE, J., BANGERT, S., AND KLEIMAN, S. PROMATLAB, Users Guzde. The MathWorks, Inc., 1987.
	13	SHAMPINE, L. F. Stiffness and nonstiff differential equation solvers. In Numerische Behandlrtng yon Dzfferentzalgleichungen, L. Collatz, Ed. Information Series of Numermal Mathematics 27, Birkhauser Verlag, Basel, 1975, pp. 287 301
	14	T. Söderström , P. Stoica, System identification, Prentice-Hall, Inc., Upper Saddle River, NJ, 1988
	15	WATTS, H. A Step size control in ordinary differential equation solvers. Trans. Soc. Comput. Szmul. 1, 1, (May 1984), 15 25.
	16	ZONNEVELD, J. A. Automatic numerical mtegTation. Akademisch Proefschrift, Matematisch Centrum, Amsterdam, 1964.

CITED BY 12

	Roger B. Sidje, Expokit: a software package for computing matrix exponentials, ACM Transactions on Mathematical Software (TOMS), v.24 n.1, p.130-156, March 1998
	Kjell Gustafsson, Control-theoretic techniques for stepsize selection in implicit Runge-Kutta methods, ACM Transactions on Mathematical Software (TOMS), v.20 n.4, p.496-517, Dec. 1994
	P. M. Burrage , R. Herdiana , K. Burrage, Adaptive stepsize based on control theory for stochastic differential equations, Journal of Computational and Applied Mathematics, v.170 n.2, p.317-336, 15 September 2004
	Gustaf Söderlind, Digital filters in adaptive time-stepping, ACM Transactions on Mathematical Software (TOMS), v.29 n.1, p.1-26, March 2003
	Nicola Guglielmi, Open issues in devising software for the numerical solution of implicit delay differential equations, Journal of Computational and Applied Mathematics, v.185 n.2, p.261-277, 15 January 2006
	Gustaf Söderlind , Lina Wang, Evaluating numerical ODE/DAE methods, algorithms and software, Journal of Computational and Applied Mathematics, v.185 n.2, p.244-260, 15 January 2006
	Gustaf Söderlind , Lina Wang, Adaptive time-stepping and computational stability, Journal of Computational and Applied Mathematics, v.185 n.2, p.225-243, 15 January 2006
	Gustaf Söderlind, Time-step selection algorithms: adaptivity, control, and signal processing, Applied Numerical Mathematics, v.56 n.3, p.488-502, March 2006
	Lars Ferm , Per Lötstedt, Space---Time Adaptive Solution of First Order PDES, Journal of Scientific Computing, v.26 n.1, p.83-110, January 2006
	L. F. Shampine, Error Estimation and Control for ODEs, Journal of Scientific Computing, v.25 n.1, p.3-16, October 2005
	M. H. Carpenter , C. A. Kennedy , Hester Bijl , S. A. Viken , Veer N. Vatsa, Fourth-Order Runge---Kutta Schemes for Fluid Mechanics Applications, Journal of Scientific Computing, v.25 n.1, p.157-194, October 2005
	Alex Kanevsky , Mark H. Carpenter , David Gottlieb , Jan S. Hesthaven, Application of implicit-explicit high order Runge-Kutta methods to discontinuous-Galerkin schemes, Journal of Computational Physics, v.225 n.2, p.1753-1781, August, 2007