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Multistep Hermite collocation methods for solving Volterra Integral Equations

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Abstract

In this paper, we propose a new class of multistep collocation methods for solving nonlinear Volterra Integral Equations, based on Hermite interpolation. These methods furnish an approximation of the solution in each subinterval by using approximated values of the solution, as well as its first derivative, in the r previous steps and m collocation points. Convergence order of the new methods is determined and their linear stability is analyzed. Some numerical examples show efficiency of the methods.

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Authors and Affiliations

  1. Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran

    Somayyeh Fazeli, Gholamreza Hojjati & Sedaghat Shahmorad

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  1. Somayyeh Fazeli
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  2. Gholamreza Hojjati
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  3. Sedaghat Shahmorad
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Correspondence to Gholamreza Hojjati.

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Fazeli, S., Hojjati, G. & Shahmorad, S. Multistep Hermite collocation methods for solving Volterra Integral Equations. Numer Algor 60, 27–50 (2012). https://doi.org/10.1007/s11075-011-9510-5

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  • DOI: https://doi.org/10.1007/s11075-011-9510-5

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