A block-by-block method for Volterra integro-differential equations with weakly-singular kernel
Author:
Athena Makroglou
Journal:
Math. Comp. 37 (1981), 95-99
MSC:
Primary 65R20
DOI:
https://doi.org/10.1090/S0025-5718-1981-0616362-2
MathSciNet review:
616362
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Abstract | References | Similar Articles | Additional Information
Abstract: The theory of a block-by-block method for solving Volterra integro-differential equations with continuous kernels (see Makroglou [4], [5]) is adapted to Volterra integro-differential equations with weakly-singular kernels, and a rate of convergence is given.
- Christopher T. H. Baker, The numerical treatment of integral equations, Clarendon Press, Oxford, 1977. Monographs on Numerical Analysis. MR 0467215
- Frank de Hoog and Richard Weiss, Asymptotic expansions for product integration, Math. Comp. 27 (1973), 295–306. MR 329207, DOI https://doi.org/10.1090/S0025-5718-1973-0329207-0
- Peter Linz, Numerial methods for Volterra integral equations with singular kernels, SIAM J. Numer. Anal. 6 (1969), 365–374. MR 260222, DOI https://doi.org/10.1137/0706034 A. Makroglou, Numerical Solution of Volterra Integro-Differential Equations, Ph.D. thesis, Univ. of Manchester, U.K., Feb. 1977.
- Athena Makroglou, Convergence of a block-by-block method for nonlinear Volterra integro-differential equations, Math. Comp. 35 (1980), no. 151, 783–796. MR 572856, DOI https://doi.org/10.1090/S0025-5718-1980-0572856-9 R. Weiss, Numerical Procedures for Volterra Integral Equations, Ph.D. thesis, Computer Centre, Australian National University, Canberra, 1972.
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Article copyright:
© Copyright 1981
American Mathematical Society
