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Modified Euler’s method with a graded mesh for a class of Volterra integral equations with weakly singular kernel

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Abstract

A modified Euler’s method applied on a graded mesh is considered for numerical solution of a class of Volterra integral equations with weakly singular kernel which depends on a parameter μ > 0. It is shown that the convergence rate of the considered method is higher than those of earlier ones for the case when μ ≤ 1. The convergence rate is also obtained in the case μ > 1. Using some numerical examples, we illustrate the theoretical results.

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  1. Department of Basic Sciences, Iranian Institute for Encyclopedia Research, PO Box 14655-478, Tehran, Iran

    Hassan Majidian

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  1. Hassan Majidian
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Correspondence to Hassan Majidian.

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Majidian, H. Modified Euler’s method with a graded mesh for a class of Volterra integral equations with weakly singular kernel. Numer Algor 67, 405–422 (2014). https://doi.org/10.1007/s11075-013-9799-3

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  • DOI: https://doi.org/10.1007/s11075-013-9799-3

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