On the discretization of differential and Volterra integral equations with variable delay

BIT Numerical Mathematics

Volumn 37, Issue 1, 1997, Pages 1-12

  Brunner, Hermann ^a  

^a MEMORIAL UNIVERSITY OF NEWFOUNDLAND   (Canada)

Author keywords

Collocation; Delay differential and integral equations; Implicit Runge Kutta methods; Optimal order; Variable delay

Indexed keywords

EID: 0002039485     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02510168     Document Type: Article

References (18)

1. G. Andreoli, Sulle equazione integrali, Rend. Palermo, 37 (1914), pp. 76-112.
2. N. Baddour and H. Brunner, Continuous Volterra-Runge-Kutta methods for integral equations with pure delay, Computing, 50 (1993), pp. 213-227.
3. A. Bellen, One-step collocation for delay differential equations, J. Comput. Appl. Math., 10 (1984), pp. 275-283.
4. J. G. Blom and H. Brunner, The numerical solution of nonlinear Volterra integral equations of the second kind by collocation and iterated collocation methods, SIAM J. Sci. Statist, Comput., 8 (1987), pp. 806-830.
5. H. Brunner, Iterated collocation methods and their discretizations for Volterra integral equations, SIAM J. Numer. Anal., 21 (1984), pp. 1132-1145.
6. H. Brunner, Iterated collocation methods for Volterra integral equations with delay arguments, Math. Comp., 62 (1994), pp. 581-599.
7. H. Brunner and P. J. Van der Houwen, The Numerical Solution of Volterra Equations, CWI Monograph 3, North-Holland, Amsterdam, 1986.
8. M. D. Buhmann and A. Iserles, On the dynamics of a discretized neutral equation, IMA J. Numer. Anal., 12 (1992), pp. 339-363.
9. M. D. Buhmann and A. Iserles, Numerical analysis of functional differential equations with a variable delay, in: Numerical Analysis 1991 (D. F. Griffiths and G. A. Watson, eds.), Pitman Research Notes in Math., Vol. 260, Longman, Harlow, 1992: pp. 17-33.
10. M. D. Buhmann, A. Iserles and S.P. Nørsett, Runge-Kutta methods for neutral differential equations, in Contributions in Numerical Analysis (R. P. Agarwal, ed.), World Scientific Series in Applicable Analysis, Vol. 2, World Scientific Publishing Co., River Edge, N.J., 1993: pp. 85-98.
11. 0 g(x, y, φ(y))dy, Internat. J. Math. Math. Sci., 14 (1990), pp. 27-44.
12. L. Fox, D. F. Mayers, J. R. Ockendon, and A. B. Tayler, On a functional differential equation, J. Inst. Math. Appl., 8 (1971), pp. 271-307.
13. E. Hairer and E. Wanner, Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems, Springer-Verlag, Heidelberg-New York, 1991.
14. A. Iserles, On the generalized pantograph functional differential equation, Europ. J. Appl. Math., 4 (1993), pp. 1-38.
15. A. Iserles, Numerical analysis of delay differential equations with variable delays, Numerical Analysis Report DAMTP 1993/NA7, University of Cambridge, 1993.
16. A. Iserles and S. P. Nørsett, Order Stars, Chapman & Hall, London, 1991.
17. T. Kato and J. B. McLeod, The functional-differential equation y′(x) = ay(λx) + by(x), Bull. Amer. Math. Soc., 77 (1971), pp. 891-937.
18. Y. Liu, Stability analysis of θ-methods for neutral functional-differential equations, Numer. Math., 70 (1995), pp. 473-485.