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Numerical solutions of integral and integro-differential equations using Legendre polynomials

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Abstract

In this paper, a finite Legendre expansion is developed to solve singularly perturbed integral equations, first order integro-differential equations of Volterra type arising in fluid dynamics and Volterra delay integro-differential equations. The error analysis is derived. Numerical results and comparisons with other methods in literature are considered.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt

    A. H. Khater

  2. Department of Mathematics, Faculty of Science, El-Minia University, El-Minia, Egypt

    A. B. Shamardan

  3. Department of Physics, CGB, University of Antwerp, 2020, Antwerp, Belgium

    D. K. Callebaut

  4. Department of Mathematics, Faculty of Science, Fayoum University, Fayoum, Egypt

    M. R. A. Sakran

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  1. A. H. Khater
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  2. A. B. Shamardan
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  3. D. K. Callebaut
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  4. M. R. A. Sakran
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Correspondence to A. H. Khater.

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Khater, A.H., Shamardan, A.B., Callebaut, D.K. et al. Numerical solutions of integral and integro-differential equations using Legendre polynomials. Numer Algor 46, 195–218 (2007). https://doi.org/10.1007/s11075-007-9130-2

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