Three-Dimensional Nonlinear Integral Operator with the Modelling of Majorant Function

In this paper, the process for finding an approximate solution of nonlinear three-dimensional (3D) Volterra type integral operator equation (N3D-VIOE) in R3 is introduced. The modelling of the majorant function (MF) with the modified Newton method (MNM) is employed to convert N3D-VIOE to the linear...

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Published inMajallat Baghdād lil-ʻulūm Vol. 18; no. 2; p. 296
Main Authors Hameed, Hameed Husam, Al-Saedi, Hayder M
Format Journal Article
LanguageEnglish
Published University of Baghdad, College of Science for Women 01.06.2021
Subjects
Majorant function, Modified Newton method, Non-linear integral operator
Online AccessGet full text
ISSN2078-8665
2411-7986
DOI10.21123/bsj.2021.18.2.0296

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Abstract In this paper, the process for finding an approximate solution of nonlinear three-dimensional (3D) Volterra type integral operator equation (N3D-VIOE) in R3 is introduced. The modelling of the majorant function (MF) with the modified Newton method (MNM) is employed to convert N3D-VIOE to the linear 3D Volterra type integral operator equation (L3D-VIOE). The method of trapezoidal rule (TR) and collocation points are utilized to determine the approximate solution of L3D-VIOE by dealing with the linear form of the algebraic system. The existence of the approximate solution and its uniqueness are proved, and illustrative examples are provided to show the accuracy and efficiency of the model. Mathematical Subject Classification (2010):  45P05, 45G10, 47H99
AbstractList In this paper, the process for finding an approximate solution of nonlinear three-dimensional (3D) Volterra type integral operator equation (N3D-VIOE) in R3 is introduced. The modelling of the majorant function (MF) with the modified Newton method (MNM) is employed to convert N3D-VIOE to the linear 3D Volterra type integral operator equation (L3D-VIOE). The method of trapezoidal rule (TR) and collocation points are utilized to determine the approximate solution of L3D-VIOE by dealing with the linear form of the algebraic system. The existence of the approximate solution and its uniqueness are proved, and illustrative examples are provided to show the accuracy and efficiency of the model. Mathematical Subject Classification (2010):  45P05, 45G10, 47H99
Author Al-Saedi, Hayder M
Hameed, Hameed Husam
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SubjectTerms Majorant function, Modified Newton method, Non-linear integral operator
Title Three-Dimensional Nonlinear Integral Operator with the Modelling of Majorant Function
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