Legendre spectral collocation method for solving nonlinear fractional Fredholm integro-differential equations with convergence analysis-Reference-Cited by-同舟云学术

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

Published:2024 Issue:4 Volume:9 Page:7973-8000
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Tedjani A. H.¹,Amin A. Z.²,Abdel-Aty Abdel-Haleem³,Abdelkawy M. A.¹⁴,Mahmoud Mona⁵

Affiliation:

1. Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia

2. Department of Mathematical Sciences, Faculty of Science & Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia

3. Department of Physics, College of Sciences, University of Bisha, P.O. Box 344, Bisha 61922, Saudi Arabia

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

5. Department of Physics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia

Abstract

<abstract><p>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.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

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