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Research Article | Open Access

A nonstandard compact finite difference method for a truncated Bratu–Picard model

Maryam Arabameri1, Raziyeh Gharechahi1, Taher A. Nofal2, Hijaz Ahmad3,4,5,6( )
Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran
Department of Mathematics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
Near East University, Operational Research Center in Healthcare, TRNC Mersin 10, Nicosia, 99138, Turkey
Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah, 42351, Saudi Arabia
Department of Mathematics, College of Science, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul 02841, South Korea
Department of Technical Sciences, Western Caspian University, Baku 1001, Azerbaijan
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Abstract

In this paper, we used the nonstandard compact finite difference method to numerically solve one-dimensional truncated Bratu-Picard equations and discussed the convergence analysis of the proposed method. Depending on the parameters in the mentioned equation, it may have no solution, one solution, or two solutions; also, it may have infinitely many solutions. The numerical results show that our method covers all mentioned aspects depending on the parameters in the equation.

Keywords

truncated Bratu–Picard modelboundary value problemsnonstandard compact finite difference methods
CLC number: 34B15, 26E35, 34A34, 65L12

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AIMS Mathematics
Volume 9 Issue 10,
October 2024
Pages 27557-27576
DOI: 10.3934/math.20241338

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Cite this article:
Arabameri M, Gharechahi R, Nofal TA, et al. A nonstandard compact finite difference method for a truncated Bratu–Picard model. AIMS Mathematics, 2024, 9(10): 27557-27576. https://doi.org/10.3934/math.20241338

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Received: 04 May 2024
Revised: 30 July 2024
Accepted: 09 August 2024
Published: 15 October 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)