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General 2 × 2 system of nonlinear integral equations and its approximate solution

In this note, we consider a general 2 × 2 system of nonlinear Volterra type integral equations. The modified Newton method (modified NM) is used to reduce the nonlinear problems into 2 × 2 linear system of algebraic integral equations of Volterra type. The latter equation is solved by discretization...

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Main Authors:	Eshkuvatov, Z. K., Hameed, Hameed Husam, Taib, B. M., Nik Long, N. M. A.
Format:	Article
Published:	2019
Online Access:	http://psasir.upm.edu.my/id/eprint/79977/ https://www.sciencedirect.com/science/article/pii/S0377042719302201
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id	my.upm.eprints.79977
record_format	eprints
spelling	my.upm.eprints.799772023-04-14T02:02:19Z http://psasir.upm.edu.my/id/eprint/79977/ General 2 × 2 system of nonlinear integral equations and its approximate solution Eshkuvatov, Z. K. Hameed, Hameed Husam Taib, B. M. Nik Long, N. M. A. In this note, we consider a general 2 × 2 system of nonlinear Volterra type integral equations. The modified Newton method (modified NM) is used to reduce the nonlinear problems into 2 × 2 linear system of algebraic integral equations of Volterra type. The latter equation is solved by discretization method. Nystrom method with Gauss–Legendre quadrature is applied for the kernel integrals and Newton forwarded interpolation formula is used for finding values of unknown functions at the selected node points. Existence and uniqueness solution of the problems are proved and accuracy of the quadrature formula together with convergence of the proposed method are obtained. Finally, numerical examples are provided to show the validity and efficiency of the method presented. Numerical results reveal that the proposed methods is efficient and accurate. Comparisons with other methods for the same problem are also presented. 2019 Article PeerReviewed Eshkuvatov, Z. K. and Hameed, Hameed Husam and Taib, B. M. and Nik Long, N. M. A. (2019) General 2 × 2 system of nonlinear integral equations and its approximate solution. pp. 528-546. https://www.sciencedirect.com/science/article/pii/S0377042719302201 10.1016/j.cam.2019.04.025
institution	Universiti Putra Malaysia
building	UPM Library
collection	Institutional Repository
continent	Asia
country	Malaysia
content_provider	Universiti Putra Malaysia
content_source	UPM Institutional Repository
url_provider	http://psasir.upm.edu.my/
description	In this note, we consider a general 2 × 2 system of nonlinear Volterra type integral equations. The modified Newton method (modified NM) is used to reduce the nonlinear problems into 2 × 2 linear system of algebraic integral equations of Volterra type. The latter equation is solved by discretization method. Nystrom method with Gauss–Legendre quadrature is applied for the kernel integrals and Newton forwarded interpolation formula is used for finding values of unknown functions at the selected node points. Existence and uniqueness solution of the problems are proved and accuracy of the quadrature formula together with convergence of the proposed method are obtained. Finally, numerical examples are provided to show the validity and efficiency of the method presented. Numerical results reveal that the proposed methods is efficient and accurate. Comparisons with other methods for the same problem are also presented.
format	Article
author	Eshkuvatov, Z. K. Hameed, Hameed Husam Taib, B. M. Nik Long, N. M. A.
spellingShingle	Eshkuvatov, Z. K. Hameed, Hameed Husam Taib, B. M. Nik Long, N. M. A. General 2 × 2 system of nonlinear integral equations and its approximate solution
author_facet	Eshkuvatov, Z. K. Hameed, Hameed Husam Taib, B. M. Nik Long, N. M. A.
author_sort	Eshkuvatov, Z. K.
title	General 2 × 2 system of nonlinear integral equations and its approximate solution
title_short	General 2 × 2 system of nonlinear integral equations and its approximate solution
title_full	General 2 × 2 system of nonlinear integral equations and its approximate solution
title_fullStr	General 2 × 2 system of nonlinear integral equations and its approximate solution
title_full_unstemmed	General 2 × 2 system of nonlinear integral equations and its approximate solution
title_sort	general 2 × 2 system of nonlinear integral equations and its approximate solution
publishDate	2019
url	http://psasir.upm.edu.my/id/eprint/79977/ https://www.sciencedirect.com/science/article/pii/S0377042719302201
_version_	1763298015886442496
score	13.211869

General 2 × 2 system of nonlinear integral equations and its approximate solution

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