Stability in the numerical solution of linear parabolic equations with a delay term

BIT Numerical Mathematics

Volumn 41, Issue 1, 2001, Pages 191-206

  Zubik Kowal, Barbara ^a,b  

^a UNIVERSITY OF GDA SK   (Poland)

^b INSTITUTE OF MATHEMATICS   (Poland)

Author keywords

Contractivity properties; Error bounds; Error propagation; Numerical stability; Parabolic equations with delay terms

Indexed keywords

EID: 0242401393     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1021930104326     Document Type: Article

References (17)

1. A. N. Al-Mutib, Stability properties of numerical methods for solving delay differential equations, J. Comput. Appl. Math., 10 (1984), pp. 71-79.
2. V. K. Barwell, Special stability problems for functional differential equations, BIT, 15 (1975), pp. 130-135.
3. D. J. Higham and T. Sardar, Existence and stability of fixed points for a discretized nonlinear reaction-diffusion equation with delay, Appl. Numer. Math., 18 (1995), pp. 155-173.
4. K. J. in't Hout, On the stability of adaptations of Runge-Kutta methods to systems of delay differential equations, Appl. Numer. Math., 22 (1996), pp. 237-250.
5. K. J. in't Hout, Stability analysis of Runge-Kutta methods for systems of delay differential equations, IMA J. Numer. Anal., 17 (1997), pp. 17-27.
6. K. J. in't Hout, The stability of θ-methods for systems of delay differential equations, Ann. Numer. Math., 1 (1994), pp. 323-334.
7. M. Z. Liu and M. N. Spijker, The stability of the θ-methods in the numerical solution of delay differential equations, IMA J. Num. Anal., 10 (1990), pp. 31-48.
8. Z. Jackiewicz, Asymptotic stability analysis of θ-methods for functional differential equations, Numer. Math., 43 (1984), pp. 389-396.
9. M. N. Spijker, Numerical stability, resolvent conditions and delay differential equations, Appl. Numer. Math., 24, (1997), pp. 233-246.
10. E. G. Van den Heuvel, Using resolvent conditions to obtain new stability results for θ-methods for delay differential equations, IMA J. Numer. Anal., to appear.
11. E. G. Van den Heuvel, New stability results for Runge-Kutta methods adapted to delay differential equations, Appl. Numer. Math., 34, (2000), pp. 293-308.
12. P. J. Van der Houwen and B. P. Sommeijer, Stability in linear multistep methods for pure delay equations, J. Comput. Appl. Math, 10 (1984), pp. 55-63.
13. D. S. Watanabe and M. G. Roth, The stability of difference formulas for delay differential equations, SIAM. Numer. Anal., 22 (1985), pp. 132-145.
14. J. Wu, Theory and Applications of Partial Functional Differential Equations, Springer-Verlag, New York, 1996.
15. M. Zennaro, On the P-stability of one-step collocation for delay differential equations, Internat. Ser. Numer. Math., 74 (1985), pp. 334-343.
16. M. Zennaro, P-stability properties of Runge-Kutta methods for delay differential equations, Numer. Math., 49, pp. 305-318.
17. B. Zubik-Kowal, The method of lines for parabolic differential-functional equations, IMA J. Numer. Anal., 17 (1997), pp. 103-123.