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

	New theoretical conditions for solving functional nonlinear equations by linearization then discretization
International Journal of Nonlinear Analysis and Applications
مقاله 231، دوره 13، شماره 1، خرداد 2022، صفحه 2857-2869 اصل مقاله (410.67 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.24699.2800
نویسندگان
Ammar Khellaf^* ¹؛ Mohamed Zine Aissaoui²
¹Preparatory Class Department, National Polytechnic College of Constantine (Engineering College), Algeria
²Department of Mathematics, Faculty of Mathematics and Computer Science and Material Sciences, University 8 May 1945 of Guelma, Algeria
چکیده
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.
کلیدواژه‌ها
Nonlinear equation؛ Iterative methods؛ Convergence؛ Newton-Kantorovich method
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