Stability analysis of Runge-Kutta methods for systems of delay differential equations

IMA Journal of Numerical Analysis

Volumn 17, Issue 1, 1997, Pages 17-27

  In 'T Hout, K J ^a  

^a LEIDEN UNIVERSITY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

INITIAL VALUE PROBLEMS; NUMERICAL METHODS;

COMPLEX MATRICES; DELAY DIFFERENTIAL EQUATIONS; NUMERICAL PROCESS; NUMERICAL SOLUTION; STABILITY ANALYSIS;

RUNGE KUTTA METHODS;

EID: 0031506225     PISSN: 02724979     EISSN: None     Source Type: Journal    
DOI: 10.1093/imanum/17.1.17     Document Type: Article

References (24)

1. BARWELL, V. K. 1975 Special stability problems for functional differential equations. BIT 15, 130-135.
2. BICKART, T. A. 1982 P-stable and P[α, β]-stable integration/interpolation methods in the solution of retarded differential-difference equations. BIT 22, 464-476.
3. BUTCHER, J. C. 1987 The Numerical Analysis of Ordinary Differential Equations. Chichester: John Wiley & Sons.
4. DEKKER, K., & VERWER, J. G. 1984 Stability of Runge-Kutta Methods for Stiff Nonlinear Differential Equations. Amsterdam: North-Holland.
5. HAIRER, E., NØRSETT, S. P., & WANNER, G. 1993 Solving Ordinary Differential Equations I, second edn. Berlin: Springer.
6. HAIRER, E., & WANNER, G. 1991 Solving Ordinary Differential Equations II. Berlin: Springer.
7. HORN, R. A., & JOHNSON, C. R. 1991 Topics in Matrix Analysis. Cambridge: Cambridge University Press.
8. Hu, G., & MITSUI, T. 1995 Stability analysis of numerical methods for systems of neutral delay-differential equations. BIT 35, 504-515.
9. IN 'T HOUT, K. J. 1992a The stability of a class of Runge-Kutta methods for delay differential equations. Appl. Numer. Math. 9, 347-355.
10. IN 'T HOUT, K. J. 1992b A new interpolation procedure for adapting Runge-Kutta methods to delay differential equations. BIT 32, 634-649.
11. IN 'T HOUT, K. J. 1994 The stability of θ-methods for systems of delay differential equations. Ann. Numer. Math. 1, 323-334.
12. IN 'T HOUT, K. J., & SPLIKER, M. N. 1991a The θ-methods in the numerical solution of delay differential equations. Numerical Treatment of Differential Equations (Teubner-Texte zur Mathematik 121) (K. Strehmel, ed). Stuttgart: Teubner, pp 61-67.
13. IN 'T HOUT, K. J., & SPIJKER, M. N. 1991b Stability analysis of numerical methods for delay differential equations. Numer Math. 59, 807-814.
14. ISERLES, A., & STRANG, G. 1983 The optimal accuracy of difference schemes. Trans. Am. Math. Soc. 277, 779-803.
15. KOTO, T. 1994 A stability property of A-stable natural Runge-Kutta methods for systems of delay differential equations. BIT 34, 262-267.
16. LANCASTER, P., & TISMENETSKY, M. 1985 The Theory of Matrices, second edn. Orlando, FL: Academic.
17. LIU, M. Z., & SPIJKER, M. N. 1990 The stability of the θ-methods in the numerical solution of delay differential equations. IMA J. Numer. Anal. 10, 31-48.
18. LUBICH, CH., & OSTERMANN, A. 1987 Multi-grid dynamic iteration for parabolic equations. BIT 27, 216-234.
19. MIEKKALA, U., & NEVANLINNA, O. 1987a Convergence of dynamic iteration methods for initial value problems. SIAM J. Sci. Stat. Comput. 8, 459-482.
20. MIEKKALA, U., & NEVANLINNA, O. 1987b Sets of convergence and stability regions. BIT 27, 554-584.
21. STRANG, G. 1962 Trigonometric polynomials and difference methods of maximum accuracy. J. Math. Phys. 41, 147-154.
22. WATANABE, D. S., & ROTH, M. G. 1985 The stability of difference formulas for delay differential equations. SIAM J. Numer. Anal. 22, 132-145.
23. ZENNARO, M. 1985 On the P-stability of one-step collocation for delay differential equations. Int. Ser. Numer. Math. 74, 334-343.
24. ZENNARO, M. 1986 P-stability properties of Runge-Kutta methods for delay differential equations. Numer. Math. 49, 305-318.