Legendre–Gauss–Lobatto collocation method for solving multi-dimensional Fredholm integral equations

Bhrawy, A.H.; Abdelkawy, M.A.; Machado, J. A. Tenreiro; Amin, A.Z.M.

http://hdl.handle.net/10400.22/9417

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Authors

Bhrawy, A.H.

Abdelkawy, M.A.

Machado, J. A. Tenreiro

Amin, A.Z.M.

Abstract(s)

This paper reports a new spectral collocation technique for solving second kind Fredholm integral equations (FIEs). We develop a collocation scheme to approximate FIEs by means of the shifted Legendre–Gauss–Lobatto collocation (SL–GL-C) method. Moreover, we adapt the SL–GL-C algorithm to solve one dimensional second kind FIEs and system of FIEs. Two numerical algorithms are also investigated to solve the two dimensional FIEs. Extensive numerical tests illustrate the capability and high accuracy of the proposed methodologies.

Keywords

Fredholm integral equation Spectral collocation method Shifted Legendre polynomials System of Fredholm integral equations Shifted Legendre–Gauss–Lobatto Quadrature

URI

http://hdl.handle.net/10400.22/9417

Publisher

Elsevier

DOI

http://dx.doi.org/10.1016/j.camwa.2016.04.011

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ISEP - DEE - Artigos

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