A Superconvergent discontinuous Galerkin method for Volterra integro-differential equations, smooth and non-smooth kernels

Mustapha, Kassem

doi:10.1090/S0025-5718-2013-02689-0

A Superconvergent discontinuous Galerkin method for Volterra integro-differential equations, smooth and non-smooth kernels
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by Kassem Mustapha;

Math. Comp. 82 (2013), 1987-2005

DOI: https://doi.org/10.1090/S0025-5718-2013-02689-0

Published electronically: April 18, 2013

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Abstract:

We study the numerical solution for Volerra integro-differential equations with smooth and non-smooth kernels. We use an $h$-version discontinuous Galerkin (DG) method and derive nodal error bounds that are explicit in the parameters of interest. In the case of non-smooth kernel, it is justified that the start-up singularities can be resolved at superconvergence rates by using non-uniformly graded meshes. Our theoretical results are numerically validated in a sample of test problems.

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