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

Maryam Arabameri; Raziyeh Gharechahi; Taher A. Nofal; Hijaz Ahmad; Maryam Arabameri; Raziyeh Gharechahi; Taher A. Nofal; Hijaz Ahmad

doi:10.3934/math.20241338

AIMS Mathematics

2024, Volume 9, Issue 10: 27557-27576. doi: 10.3934/math.20241338

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Research article

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

1.
Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran
2.
Department of Mathematics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
3.
Near East University, Operational Research Center in Healthcare, TRNC Mersin 10, Nicosia, 99138, Turkey
4.
Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah, 42351, Saudi Arabia
5.
Department of Mathematics, College of Science, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul 02841, South Korea
6.
Department of Technical Sciences, Western Caspian University, Baku 1001, Azerbaijan

Received: 04 May 2024 Revised: 30 July 2024 Accepted: 09 August 2024 Published: 24 September 2024
MSC : 34B15, 26E35, 34A34, 65L12

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.
- truncated Bratu–Picard model,
- boundary value problems,
- nonstandard compact finite difference methods
Citation: Maryam Arabameri, Raziyeh Gharechahi, Taher A. Nofal, Hijaz Ahmad. A nonstandard compact finite difference method for a truncated Bratu–Picard model[J]. AIMS Mathematics, 2024, 9(10): 27557-27576. doi: 10.3934/math.20241338

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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.

References

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