Publication: On the Solution of Multi-Dimensional Nonlinear Integral Equation with Modified Newton Method
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Date
2017
Journal Title
Journal ISSN
Volume Title
Publisher
American Scientific Publishers
Abstract
In this note, multi-dimensional nonlinear integral equations (multi-dimensional NIEs) in Rn is considered. Implementing modified Newton method (Modified NM) reduces multi-dimensional NIEs into multi-dimensional linear integral equations (multi-dimensional LIEs), which can be solved by discritization method. Quadrature method together with collocation are used to find values of unknown functions. Existence and uniqueness solution of the problems are shown. The rate of convergence of the proposed method is proved using the principle of majorant function. Finally, numerical examples are provided and it reveals that proposed method is both accurate and effective as well as comparisons with other methods are also presented.
Description
Volume 14, Number 11
Keywords
The Modified Newton Method, Nonlinear Multi-Dimensional Integral Equations, Quadrature Formula, The Majorant Function