The discretization of neutral functional integro-differential equations by collocation methods

Zeitschrift für Analysis und ihre Anwendungen

Volumn 18, Issue 2, 1999, Pages 393-406

  Brunner, H ^a  

^a MEMORIAL UNIVERSITY OF NEWFOUNDLAND   (Canada)

Author keywords

Collocation methods; Neutral functional integro differential equations; Volterra integral equations with delay

Indexed keywords

EID: 22644449317     PISSN: 02322064     EISSN: None     Source Type: Journal    
DOI: 10.4171/ZAA/889     Document Type: Article

References (21)

1. Brunner, H.: Discretization of Volterra integral equations of the first kind (II). Numer. Math. 30(1978), 117 - 136.
2. Brunner, H.: Iterated collocation methods for Volterra integral equations with delay arguments. Math. Comp. 62 (1994), 581 - 599.
3. Brunner, H.: The numerical solution of neutral Volterra integro-differential equations with delay arguments. Ann. Numer. Math. 1 (1994), 309 - 322.
4. Brunner, H.: On systems of Volterra difference equations associated with collocation methods for weakly singular Volterra integral equations. In: Proc. Third Intern. Conf. Difference Equ. Appl., Taipei 1997 (to appear).
5. Brunner, H.: The use of splines in the numerical solution of differential and Volterra integral equations. In: Spline Functions and the Theory of Wavelets, Vol. I and II, Montréal 1996 (ed.: S. Dubuc; CRM Proceedings and Lecture Notes: Vol. 17). Providence (RI): Amer. Math. Soc. 1999 (to appear).
6. Brunner, H. and P. J. van der Houwen: The Numerical Solution of Volterra Equations (CWI Monographs: Vol. 3). Amsterdam: North-Holland 1986.
7. Brunner, H. and N. Yan: On global superconvergence of iterated collocation solutions to linear second-kind Volterra integral equations. J. Comput. Appl. Math. 67 (1996), 185 - 189.
8. Burns, J. A., Herdman, T. L. and H. W. Stech: Linear functional differential equations as semigroups on product spaces. SIAM J. Math. Anal. 14 (1983), 98 - 116.
9. Burns, J. A., Herdman, T. L. and J. Turi: Neutral functional integro-dijferential equations with weakly singular kernels. J. Math. Anal. Appl. 145 (1990), 371 - 401.
10. Hale, J. K. and S. M. Verduyn Lunel: Introduction to Functional Differential Equations (Appl. Math. Sci.: Vol. 99). New York: Springer-Verlag 1993.
11. Henrici, P.: Elements of Numerical Analysis. New York: John Wiley & Sons 1964.
12. Ito, K. and J. Turi: Numerical methods for a class of singular integro-differential equations based on semigroup approximation. SIAM J. Numer. Anal. 28 (1991), 1698 - 1722.
13. Janno, J. and L. v. Wolfersdorf: Inverse problems for identification of memory kernels in viscoelasticity. Math. Methods Appl. Sci. 20 (1997), 291 - 314.
14. Janno, J. and L. v. Wolfersdorf: Identification of weakly singular memory kernels in heat conduction., Z.Angew. Math. Mech. (ZAMM) 77 (1997), 243 - 257.
15. Kappel, F. and K. P. Zhang: On neutral functional differential equations with nonatomic difference operator. J. Math. Anal. Appl. 113 (1986), 311 - 343.
16. Kauthen, J.-P. and H. Brunner: Continuous collocation approximations to solutions of first kind Volterra equations. Math. Comp. 66 (1997), 1441 - 1459.
17. Ortega, J. M.: Numerical Analysis: A Second Course. New York: Academic Press 1972.
18. Unger, F.and L. v. Wolfersdorf: Inverse Probleme zur Identifikation von Memory-Kernen. Freiberger Forschungshefte, C 458 Mathematik, Technische Universität Bergakademie Freiberg 1995.
19. Unterreiter, A.: Volterra integral equation models for semiconductor devices. Math. Methods Appl. Sci. 19 (1996), 425 - 450.
20. Wolfersdorf, L. von: On identification of memory kernels in linear theory of heat conduction. Math. Methods Appl. Sci. 17 (1994), 919 - 932.
21. Zennaro, M.: Delay differential equations: theory and numerics. In: Theory and Numerics of Ordinary and Partial Differential Equations (ed.: M. Ainsworth; Advances in Numerical Analysis: Vol. 4). Oxford: Clarendon Press 1995, pp. 291 - 333.