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Stability of Numerical Solutions for Abel–Volterra Integral Equations of the Second Kind

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Abstract

We analyze the stability of convolution quadrature methods for weakly singular Volterra integral equations with respect to a linear test equation. We prove that the asymptotic behavior of the numerical solution replicates the one of the continuous problem under some restriction on the stepsize. Numerical examples illustrate the theoretical results.

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Authors and Affiliations

  1. Dipartimento di Matematica e Applicazioni, Università degli Studi di Napoli “Federico II”, Via Cintia, 80126, Naples, Italy

    G. Izzo & E. Messina

  2. C.N.R. National Research Council of Italy, Institute for Computational Application “Mauro Picone”, Via P. Castellino 111, 80131, Naples, Italy

    A. Vecchio

Authors
  1. G. Izzo
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  2. E. Messina
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  3. A. Vecchio
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Correspondence to G. Izzo.

Additional information

G. Izzo, E. Messina and A. Vecchio are members of the INdAM Research group GNCS.

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Izzo, G., Messina, E. & Vecchio, A. Stability of Numerical Solutions for Abel–Volterra Integral Equations of the Second Kind. Mediterr. J. Math. 15, 113 (2018). https://doi.org/10.1007/s00009-018-1149-1

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  • DOI: https://doi.org/10.1007/s00009-018-1149-1

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