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Numerical solution of Volterra integral equations with singularities

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Abstract

The numerical solution of linear Volterra integral equations of the second kind is discussed. The kernel of the integral equation may have weak diagonal and boundary singularities. Using suitable smoothing techniques and polynomial splines on mildly graded or uniform grids, the convergence behavior of the proposed algorithms is studied and a collection of numerical results is given.

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Authors and Affiliations

  1. Institute of Mathematics, University of Tartu, J. Liivi 2, Tartu, 50409, Estonia

    Marek Kolk & Arvet Pedas

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  1. Marek Kolk
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  2. Arvet Pedas
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Correspondence to Marek Kolk.

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Dedicated to Professor Hermann Brunner on his 70th birthday

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Kolk, M., Pedas, A. Numerical solution of Volterra integral equations with singularities. Front. Math. China 8, 239–259 (2013). https://doi.org/10.1007/s11464-013-0292-z

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  • DOI: https://doi.org/10.1007/s11464-013-0292-z

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