Newton-Kantorovich method for solving one- and two-dimensional nonlinear Volterra integral equations of the second kind

The problems of nonlinear Volterra integral equations (VIEs) which consist of one dimensional nonlinear VIE, system of 2×2 nonlinear VIEs, system of n × n nonlinear VIEs, and two dimensional nonlinear VIE, with smooth unknown functions and continuous bounded given functions are discussed. The Newton...

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Main Author:	Hameed, Hameed Husam
Format:	Thesis
Language:	English
Published:	2016
Subjects:	Iterative methods (Mathematics) Numerical analysis Volterra equations - Numerical solutions
Online Access:	http://psasir.upm.edu.my/id/eprint/75452/1/FS%202016%209%20-%20IR.pdf
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id	my-upm-ir.75452
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spelling	my-upm-ir.754522019-10-18T07:34:55Z Newton-Kantorovich method for solving one- and two-dimensional nonlinear Volterra integral equations of the second kind 2016-01 Hameed, Hameed Husam The problems of nonlinear Volterra integral equations (VIEs) which consist of one dimensional nonlinear VIE, system of 2×2 nonlinear VIEs, system of n × n nonlinear VIEs, and two dimensional nonlinear VIE, with smooth unknown functions and continuous bounded given functions are discussed. The Newton-Kantorovich method (NKM) is used to linearize the problems. Then the Nystrom-type Gauss-Legendre quadrature formula (QF) is used to solve the linearized equations and systems. New majorant functions are found for some problems which lead to the increment of convergence interval. The new approach based on the subcollocation method is developed and motivation leads to high accurate approximate solutions. The existence and uniqueness of solution are proved and error estimation and rate of convergence are obtained. Numerical examples show that our results are coincided with the theoretical finding. Iterative methods (Mathematics) Numerical analysis Volterra equations - Numerical solutions 2016-01 Thesis http://psasir.upm.edu.my/id/eprint/75452/ http://psasir.upm.edu.my/id/eprint/75452/1/FS%202016%209%20-%20IR.pdf text en public doctoral Universiti Putra Malaysia Iterative methods (Mathematics) Numerical analysis Volterra equations - Numerical solutions
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
topic	Iterative methods (Mathematics) Numerical analysis Volterra equations - Numerical solutions
spellingShingle	Iterative methods (Mathematics) Numerical analysis Volterra equations - Numerical solutions Hameed, Hameed Husam Newton-Kantorovich method for solving one- and two-dimensional nonlinear Volterra integral equations of the second kind
description	The problems of nonlinear Volterra integral equations (VIEs) which consist of one dimensional nonlinear VIE, system of 2×2 nonlinear VIEs, system of n × n nonlinear VIEs, and two dimensional nonlinear VIE, with smooth unknown functions and continuous bounded given functions are discussed. The Newton-Kantorovich method (NKM) is used to linearize the problems. Then the Nystrom-type Gauss-Legendre quadrature formula (QF) is used to solve the linearized equations and systems. New majorant functions are found for some problems which lead to the increment of convergence interval. The new approach based on the subcollocation method is developed and motivation leads to high accurate approximate solutions. The existence and uniqueness of solution are proved and error estimation and rate of convergence are obtained. Numerical examples show that our results are coincided with the theoretical finding.
format	Thesis
qualification_level	Doctorate
author	Hameed, Hameed Husam
author_facet	Hameed, Hameed Husam
author_sort	Hameed, Hameed Husam
title	Newton-Kantorovich method for solving one- and two-dimensional nonlinear Volterra integral equations of the second kind
title_short	Newton-Kantorovich method for solving one- and two-dimensional nonlinear Volterra integral equations of the second kind
title_full	Newton-Kantorovich method for solving one- and two-dimensional nonlinear Volterra integral equations of the second kind
title_fullStr	Newton-Kantorovich method for solving one- and two-dimensional nonlinear Volterra integral equations of the second kind
title_full_unstemmed	Newton-Kantorovich method for solving one- and two-dimensional nonlinear Volterra integral equations of the second kind
title_sort	newton-kantorovich method for solving one- and two-dimensional nonlinear volterra integral equations of the second kind
granting_institution	Universiti Putra Malaysia
publishDate	2016
url	http://psasir.upm.edu.my/id/eprint/75452/1/FS%202016%209%20-%20IR.pdf
_version_	1747813053437575168

Newton-Kantorovich method for solving one- and two-dimensional nonlinear Volterra integral equations of the second kind

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