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Research Article | Open Access

Fitted mesh method for singularly perturbed fourth order differential equation of convection diffusion type with integral boundary condition

V. Raja1, E. Sekar2, S. Shanmuga Priya3, B. Unyong4( )
Department of Engineering Mathematics, Koneru Lakshmaiah Education Foundation, Guntur, Andhra Pradesh, India
Department of Mathematics, Amrita School of Physical Science, Amrita Vishwa Vidyapeetham, Coimbatore 641112, Tamilnadu, India
Department of Mathematics, Cauvery College for women, Tiruchirappalli, Tamilnadu, India
Department of Mathematics, School of Science, Walailak University, Thasala, Nakhon Si Thammarat 80160, Thailand
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Abstract

This article focuses on a class of fourth-order singularly perturbed convection diffusion equations (SPCDE) with integral boundary conditions (IBC). A numerical method based on a finite difference scheme using Shishkin mesh is presented. The proposed method is close to the first-order convergent. The discrete norm yields an error estimate and theoretical estimations are tested by numerical experiments.

Keywords

fourth order differential equationnon-local boundary conditionfinite difference schemesingular perturbation problemsShishkin mesh
CLC number: 65L10, 34B10

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AIMS Mathematics
Volume 8 Issue 7,
July 2023
Pages 16691-16707
DOI: 10.3934/math.2023853

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Cite this article:
Raja V, Sekar E, Priya SS, et al. Fitted mesh method for singularly perturbed fourth order differential equation of convection diffusion type with integral boundary condition. AIMS Mathematics, 2023, 8(7): 16691-16707. https://doi.org/10.3934/math.2023853

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Received: 14 March 2023
Revised: 23 April 2023
Accepted: 04 May 2023
Published: 15 July 2023
©2023 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)