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

V. Raja; E. Sekar; S. Shanmuga Priya; B. Unyong; V. Raja; E. Sekar; S. Shanmuga Priya; B. Unyong

doi:10.3934/math.2023853

AIMS Mathematics

2023, Volume 8, Issue 7: 16691-16707. doi: 10.3934/math.2023853

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Research article

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

1.
Department of Engineering Mathematics, Koneru Lakshmaiah Education Foundation, Guntur, Andhra Pradesh, India
2.
Department of Mathematics, Amrita School of Physical Science, Amrita Vishwa Vidyapeetham, Coimbatore 641112, Tamilnadu, India
3.
Department of Mathematics, Cauvery College for women, Tiruchirappalli, Tamilnadu, India
4.
Department of Mathematics, School of Science, Walailak University, Thasala, Nakhon Si Thammarat 80160, Thailand

Received: 14 March 2023 Revised: 23 April 2023 Accepted: 04 May 2023 Published: 12 May 2023
MSC : 65L10, 34B10

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.
- fourth order differential equation,
- non-local boundary condition,
- finite difference scheme,
- singular perturbation problems,
- Shishkin mesh
Citation: V. Raja, E. Sekar, S. Shanmuga Priya, B. Unyong. Fitted mesh method for singularly perturbed fourth order differential equation of convection diffusion type with integral boundary condition[J]. AIMS Mathematics, 2023, 8(7): 16691-16707. doi: 10.3934/math.2023853

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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.

References

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