New theoretical conditions for solving functional nonlinear equations by linearization then discretization

Khellaf, Ammar; Aissaoui, Mohamed Zine

doi:10.22075/ijnaa.2022.24699.2800

New theoretical conditions for solving functional nonlinear equations by linearization then discretization

Document Type : Research Paper

Authors

Ammar Khellaf ¹

Mohamed Zine Aissaoui ²

¹ Preparatory Class Department, National Polytechnic College of Constantine (Engineering College), Algeria

² Department of Mathematics, Faculty of Mathematics and Computer Science and Material Sciences, University 8 May 1945 of Guelma, Algeria

10.22075/ijnaa.2022.24699.2800

Abstract

In this paper, we propose to solve nonlinear functional equations given in an infinite-dimensional Banach space by linearizing first and then discretizing the linear iterative equations. We establish new sufficient conditions which provide new criteria for dealing with convergence results. These conditions define a class of discretization schemes. Some numerical examples confirm the theoretical results by treating an integro-differential equation.

Keywords

Nonlinear equation

Iterative methods

Convergence

Newton-Kantorovich method

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