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: 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.

**[1]**C. T. H. Baker,*The Numerical Treatment of Integral Equations*, Clarendon Press, Oxford, 1977. MR**0467215 (57:7079)****[2]**F. de Hoog & R. Weiss, "Asymptotic expansions for product integration,"*Math. Comp.*, v. 27, 1973, pp. 295-306. MR**0329207 (48:7549)****[3]**P. Linz, "Numerical methods for Volterra integral equations with singular kernels,"*SIAM J. Numer. Anal.*, v. 6, 1969, pp. 365-374. MR**41**#4850. MR**0260222 (41:4850)****[4]**A. Makroglou,*Numerical Solution of Volterra Integro-Differential Equations*, Ph.D. thesis, Univ. of Manchester, U.K., Feb. 1977.**[5]**A. Makroglou, "Convergence of a block-by-block method for nonlilnear Volterra integro-differential equations,"*Math. Comp.*, v. 35, 1980, pp. 783-796. MR**572856 (81g:65180)****[6]**R. Weiss,*Numerical Procedures for Volterra Integral Equations*, Ph.D. thesis, Computer Centre, Australian National University, Canberra, 1972.

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DOI:
https://doi.org/10.1090/S0025-5718-1981-0616362-2

Article copyright:
© Copyright 1981
American Mathematical Society