Title of article :
New theoretical conditions for solving functional nonlinear equations by linearization then discretization
Author/Authors :
Khellaf, Amma Preparatory Class Department - National Polytechnic College of Constantine (Engineering College), Algeria , Aissaoui, Mohamed Zine Department of Mathematics - Faculty of Mathematics and Computer Science and Material Sciences - University 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 :
Nonlinear equation , Iterative methods , Convergence , Newton-Kantorovich method
Journal title :
International Journal of Nonlinear Analysis and Applications
