1. Three-Dimensional Nonlinear Integral Operator with the Modelling of Majorant Function
- Author
-
Hameed Husam Hameed and Hayder M. Al-Saedi
- Subjects
General Computer Science ,General Mathematics ,Science ,General Physics and Astronomy ,Majorant function, Modified Newton method, Non-linear integral operator ,010103 numerical & computational mathematics ,General Chemistry ,Function (mathematics) ,01 natural sciences ,Agricultural and Biological Sciences (miscellaneous) ,General Biochemistry, Genetics and Molecular Biology ,010101 applied mathematics ,Nonlinear system ,Operator (computer programming) ,Applied mathematics ,0101 mathematics ,Mathematics - 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
- Published
- 2021