Legendre-Gauss-Lobatto collocation method for solving multi-dimensional systems of mixed Volterra-Fredholm integral equations

A. Z. Amin; M. A. Abdelkawy; Amr Kamel Amin; António M. Lopes; Abdulrahim A. Alluhaybi; I. Hashim

doi:10.3934/math.20231063

Legendre-Gauss-Lobatto collocation method for solving multi-dimensional systems of mixed Volterra-Fredholm integral equations

A. Z. Amin
, M. A. Abdelkawy
, Amr Kamel Amin
, António M. Lopes
, Abdulrahim A. Alluhaybi
, I. Hashim

Universiti Kebangsaan
Al-Imam Muhammad Ibn Saud Islamic University
Faculty of Sciences
Umm Al-Qura University
University of Porto

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

Integral equations play a crucial role in many scientific and engineering problems, though solving them is often challenging. This paper addresses the solution of multi-dimensional systems of mixed Volterra-Fredholm integral equations (SMVF-IEs) by means of a Legendre-Gauss-Lobatto collocation method. The one-dimensional case is addressed first. Afterwards, the method is extended to two-dimensional linear and nonlinear SMVF-IEs. Several numerical examples reveal the effectiveness of the approach and show its superiority in comparison to other alternative techniques for treating SMVF-IEs.

Original language	English
Pages (from-to)	20871-20891
Number of pages	21
Journal	AIMS Mathematics
Volume	8
Issue number	9
DOIs	https://doi.org/10.3934/math.20231063
State	Published - 2023
Externally published	Yes

Keywords

shifted Legendre polynomials
shifted Legendre-Gauss-Lobatto quadrature
spectral collocation method
system of mixed Volterra-Fredholm integral equations

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10.3934/math.20231063

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title = "Legendre-Gauss-Lobatto collocation method for solving multi-dimensional systems of mixed Volterra-Fredholm integral equations",

abstract = "Integral equations play a crucial role in many scientific and engineering problems, though solving them is often challenging. This paper addresses the solution of multi-dimensional systems of mixed Volterra-Fredholm integral equations (SMVF-IEs) by means of a Legendre-Gauss-Lobatto collocation method. The one-dimensional case is addressed first. Afterwards, the method is extended to two-dimensional linear and nonlinear SMVF-IEs. Several numerical examples reveal the effectiveness of the approach and show its superiority in comparison to other alternative techniques for treating SMVF-IEs.",

keywords = "shifted Legendre polynomials, shifted Legendre-Gauss-Lobatto quadrature, spectral collocation method, system of mixed Volterra-Fredholm integral equations",

author = "Amin, \{A. Z.\} and Abdelkawy, \{M. A.\} and Amin, \{Amr Kamel\} and Lopes, \{Ant{\'o}nio M.\} and Alluhaybi, \{Abdulrahim A.\} and I. Hashim",

note = "Publisher Copyright: {\textcopyright} 2023 the Author(s), licensee AIMS Press.",

year = "2023",

doi = "10.3934/math.20231063",

language = "English",

volume = "8",

pages = "20871--20891",

journal = "AIMS Mathematics",

issn = "2473-6988",

publisher = "American Institute of Mathematical Sciences",

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}

TY - JOUR

T1 - Legendre-Gauss-Lobatto collocation method for solving multi-dimensional systems of mixed Volterra-Fredholm integral equations

AU - Amin, A. Z.

AU - Abdelkawy, M. A.

AU - Amin, Amr Kamel

AU - Lopes, António M.

AU - Alluhaybi, Abdulrahim A.

AU - Hashim, I.

PY - 2023

Y1 - 2023

N2 - Integral equations play a crucial role in many scientific and engineering problems, though solving them is often challenging. This paper addresses the solution of multi-dimensional systems of mixed Volterra-Fredholm integral equations (SMVF-IEs) by means of a Legendre-Gauss-Lobatto collocation method. The one-dimensional case is addressed first. Afterwards, the method is extended to two-dimensional linear and nonlinear SMVF-IEs. Several numerical examples reveal the effectiveness of the approach and show its superiority in comparison to other alternative techniques for treating SMVF-IEs.

AB - Integral equations play a crucial role in many scientific and engineering problems, though solving them is often challenging. This paper addresses the solution of multi-dimensional systems of mixed Volterra-Fredholm integral equations (SMVF-IEs) by means of a Legendre-Gauss-Lobatto collocation method. The one-dimensional case is addressed first. Afterwards, the method is extended to two-dimensional linear and nonlinear SMVF-IEs. Several numerical examples reveal the effectiveness of the approach and show its superiority in comparison to other alternative techniques for treating SMVF-IEs.

KW - shifted Legendre polynomials

KW - shifted Legendre-Gauss-Lobatto quadrature

KW - spectral collocation method

KW - system of mixed Volterra-Fredholm integral equations

UR - https://www.scopus.com/pages/publications/85163833723

U2 - 10.3934/math.20231063

DO - 10.3934/math.20231063

M3 - Article

AN - SCOPUS:85163833723

SN - 2473-6988

VL - 8

SP - 20871

EP - 20891

JO - AIMS Mathematics

JF - AIMS Mathematics

IS - 9

ER -

Legendre-Gauss-Lobatto collocation method for solving multi-dimensional systems of mixed Volterra-Fredholm integral equations

Abstract

Keywords

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