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

Document Type : Research Paper

Authors

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

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