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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
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.

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  • [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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Article copyright: © Copyright 1981 American Mathematical Society

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