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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 | ||
| تاریخ دریافت: 06 مهر 1400، تاریخ بازنگری: 11 مهر 1400، تاریخ پذیرش: 13 دی 1400 | ||
| 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 | ||
| مراجع | ||
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[1] L. Grammant, M. Ahues and F.D. D’Almeida, For nonlinear infinite dimensional equations which to begin with: Linearization or discretization, J. Integral Equ. Appl. 26 (2014) 413–436. [2] L. Grammant, Nonlinear integral equation of the second kind: A new version of Nystrom method, Numerical Funct. Anal. Optim. 34(5) (2013) 496–515. [3] L. Grammant, P.B. Vasconcelos and M. Ahues, A modified iterated projection method adapted to a nonlinear integral equation, Appl. Math. Comput. 276 (2016) 432–441. [4] A. Khellaf, W. Merchela and S. Benarab, New numerical process solving nonlinear infinite dimensional equations, Comput. Appl. Math. 93(1) (2020) 1–15. [5] B.V. Limaye, Functional Analysis, Second Edition, New Age International, New Delhi, 1996. [6] A. Khellaf, H. Guebbai, S. Lemita, M.Z. Aissaoui, Eigenvalues computation by the generalized spectrum method of Schro¨dinger’s operator, Comput. Appl. Math. 37 (2018) 5965–5980. [7] M. Ahues, A. Largillier and B.V. Limaye Spectral Computations for Bounded Operators, Chapman and Hall/CRC, 2001. | ||
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