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Piecewise Polynomial Collocation for Volterra Integral Equations with Logarithmic Kernels

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Numerical Mathematics and Advanced Applications 2011

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Abstract

We propose a numerical method for solving linear Volterra integral equations of the second kind with logarithmic kernels which, in addition to a diagonal singularity, may have a weak boundary singularity. The attainable order of global and local convergence of proposed algorithms is discussed and a collection of numerical results is given.

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References

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Acknowledgements

This work has been supported by Estonian Science Foundation (grant No. 9104).

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Authors and Affiliations

  1. Institute of Mathematics, University of Tartu, Tartu, Estonia

    M. Kolk & A. Pedas

Authors
  1. M. Kolk
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  2. A. Pedas
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Corresponding author

Correspondence to M. Kolk .

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Editors and Affiliations

  1. , Department of Mathematics, University of Leicester, Leicester, LE!1 7RH, United Kingdom

    Andrea Cangiani

  2. , Department of Mathematics, University of Leicester, Leicester, LE1 7RL, United Kingdom

    Ruslan L. Davidchack

  3. , Department of Mathematics, University of Leicester, Leicester, LE1 7RH, United Kingdom

    Emmanuil Georgoulis

  4. , Department of Mathematics, University of Leicester, Leicester, LE1 7RH, United Kingdom

    Alexander N. Gorban

  5. , Department of Mathematics, University of Leicester, Leicester, LE1 7RH, United Kingdom

    Jeremy Levesley

  6. , School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, United Kingdom

    Michael V. Tretyakov

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Kolk, M., Pedas, A. (2013). Piecewise Polynomial Collocation for Volterra Integral Equations with Logarithmic Kernels. In: Cangiani, A., Davidchack, R., Georgoulis, E., Gorban, A., Levesley, J., Tretyakov, M. (eds) Numerical Mathematics and Advanced Applications 2011. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33134-3_22

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