Legendre spectral collocation method for solving nonlinear fractional Fredholm integro-differential equations with convergence analysis

The main purpose of this work was to develop a spectrally accurate collocation method for solving nonlinear fractional Fredholm integro-differential equations (non-FFIDEs). A proposed spectral collocation method is based on the Legendre-Gauss-Lobatto collocation (L-G-LC) method in which the main ide...

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Bibliographic Details
Published inAIMS mathematics Vol. 9; no. 4; pp. 7973 - 8000
Main Authors Tedjani, A. H., Amin, A. Z., Abdel-Aty, Abdel-Haleem, Abdelkawy, M. A., Mahmoud, Mona
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2024
Subjects
caputo fractional derivative
convergence analysis
fractional fredholm integro-differential equation
legendre-gauss-lobatto
spectral method
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ISSN2473-6988
2473-6988
DOI10.3934/math.2024388

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Summary:The main purpose of this work was to develop a spectrally accurate collocation method for solving nonlinear fractional Fredholm integro-differential equations (non-FFIDEs). A proposed spectral collocation method is based on the Legendre-Gauss-Lobatto collocation (L-G-LC) method in which the main idea is to use Caputo derivatives and Legendre-Gauss interpolation for nonlinear FFIDEs. A rigorous convergence analysis is provided and confirmed by numerical tests. In addition, we provide some numerical test cases to demonstrate that the approach can preserve the non-smooth solution of the underlying problem.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2024388