Optimal time step control for the numerical solution of ordinary differential equations

SIAM Journal on Numerical Analysis

Volumn 33, Issue 4, 1996, Pages 1644-1653

  Utumi, Masaki ^a   Takaki, Ryuji ^b   Kawai, Toshio ^c  

^a TOSHIBA CORPORATION   (Japan)

^b TOKYO UNIVERSITY OF AGRICULTURE AND TECHNOLOGY   (Japan)

^c KEIO UNIVERSITY   (Japan)

Author keywords

Differential equation; Discretization; Error minimization; Numerical solution; Optimization; Time step

Indexed keywords

EID: 0742284633     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S003614299426358X     Document Type: Article

References (8)

1. L. S. PONTRYAGIN, V. G. BOLTYANSKII, R. E. GAMKRELIDGE, AND E. F. MISHCHENKO, The Mathematical Theory of Optimal Processors, Interscience Publishers, New York, 1962.
2. E. FEHLBERG, Klassische Runge-Kutta-formeln vierter und niedrigerer Ordnung mit Schrittweiten-Kontroll und ihre Anwendung auf Wärmeleitungs Probleme, Computing, 6 (1970), pp. 61-71.
3. K. GUSTAFSSON, Control theoretic techniques for stepsize selection in explicit Runge-Kutta methods, ACM Trans. Math. Software, 17 (1991), pp. 533-534.
4. D. MORRISON, Optimal mesh size in the numerical integration of an ordinary differential equation, J. Assoc. Comput. Mach., 9 (1962), pp. 98-103.
5. D. GREENSPAN, W. HAFNER, AND M. RIBARIC, On varying stepsize in numerical integration of first order differential equations, Numer. Math., 7 (1965), pp. 286-291.
6. C. W. GEAR, Numerical Initial Value Problems in Ordinary Differential Equations, Prentice-Hall, Englewood Cliffs, NJ, 1971.
7. B. LINDBERG, Characterization of optimal stepsize sequences for methods for stiff differential equations, SIAM J. Numer. Anal., 14 (1977), pp. 858-887.
8. B. C. BUTCHER, Optimal order and stepsize sequences, IMA J. Numer. Anal., 6 (1986), pp. 433-438.