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

Authors

Hameed Husam Hameed, The Middle Technical University/ Iraq Technical Institute of AL-suwarahFollow
Hayder M Al-Saedi, University of BaghdadFollow

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

Keywords

Majorant function, Modified Newton method, Non-linear integral operator, Three-dimensional Nonlinear Integral Operator, Three-dimensional Trapezoidal rule method. Mathematical Subject Classification (2020): 45G15, 47H99

Article Type

Article

How to Cite this Article

Hameed, Hameed Husam and Al-Saedi, Hayder M (2021) "Three-Dimensional Nonlinear Integral Operator with the Modelling of Majorant Function," Baghdad Science Journal: Vol. 18: Iss. 2, Article 13.
DOI: https://doi.org/10.21123/bsj.2021.18.2.0296