Finite difference scheme for third order singularly perturbed delay differential equation of convection diffusion type with integral boundary condition

Sekar, Elango; Tamilselvan, A.

doi:10.1007/s12190-019-01239-0

Cited by 15 publications

(13 citation statements)

References 9 publications

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“…Debala and Duressa [13] built a uniformly convergent numerical scheme for solving SPPs with nonlocal boundary conditions. Numerical methods for solving singularly perturbed delay differential equations (SPDDEs) are considered in Sekar and Tamilselvan [14][15][16][17]. The authors developed finite difference schemes with suitable piecewise uniform Shiskin meshes.…”

Section: Introductionmentioning

confidence: 99%

Numerical treatment of singularly perturbed parabolic partial differential equations with nonlocal boundary condition

Wondimu

Woldaregay

Dinka

et al. 2022

Front. Appl. Math. Stat.

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This paper presents numerical treatments for a class of singularly perturbed parabolic partial differential equations with nonlocal boundary conditions. The problem has strong boundary layers at x = 0 and x = 1. The nonstandard finite difference method was developed to solve the considered problem in the spatial direction, and the implicit Euler method was proposed to solve the resulting system of IVPs in the temporal direction. The nonlocal boundary condition is approximated by Simpsons 13 rule. The stability and uniform convergence analysis of the scheme are studied. The developed scheme is second-order uniformly convergent in the spatial direction and first-order in the temporal direction. Two test examples are carried out to validate the applicability of the developed numerical scheme. The obtained numerical results reflect the theoretical estimate.

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Section: Introductionmentioning

confidence: 99%

Numerical treatment of singularly perturbed parabolic partial differential equations with nonlocal boundary condition

Wondimu

Woldaregay

Dinka

et al. 2022

Front. Appl. Math. Stat.

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“…Because of this, several scholars studied SPDDEs with nonlocal boundary condition. The authors in [19] advanced a finite difference scheme on a suitable piecewise Shishkin type mesh for solving SPDDEs of convection-diffusion kind with integral boundary condition (IBC). The authors in [20] investigated a class of third order SPDDEs of the convection-diffusion kind with IBC.…”

Section: Introductionmentioning

confidence: 99%

“…The authors in [19] advanced a finite difference scheme on a suitable piecewise Shishkin type mesh for solving SPDDEs of convection-diffusion kind with integral boundary condition (IBC). The authors in [20] investigated a class of third order SPDDEs of the convection-diffusion kind with IBC. They devised a numerical method depends on FDM with Shishkin mesh.…”

Section: Introductionmentioning

confidence: 99%

Exponentially fitted numerical method for solving singularly perturbed delay reaction-diffusion problem with nonlocal boundary condition

Wondimu

Woldaregay

Duressa

et al. 2022

Preprint

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Objectives: In this article, singularly perturbed delay reaction-diffusion problem with nonlocal boundary condition is considered. The exponential fitting factor is introduced to treat the solutions inside the boundary layer which occur due to perturbation parameter. The considered problem has interior layer at x = 1 and strong boundary layers at x = 0 and x = 2. We proposed an exponentially fitted finite difference method to solve the considered problem. The nonlocal boundary condition is treated using Composite Simpson’s 1/3 rule. Result: The stability and uniform convergence analysis of the proposed approach are established. The error estimation of the developed method is shown to be second-order uniform convergent. Two test examples are carried out to validate the applicability of the developed numerical method. The numerical results reflect the theoretical estimations. AMS Subject Classification: Primary 65L11, 65L12, 65L20, 65L70.

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“…al., 2010). Finite difference scheme is established on Shishkin mesh with integral boundary conditions (Sekar and Tamilselvan, 2019).…”

Section: Introductionmentioning

confidence: 99%

Singüler Pertürbe Özellikli Konveksiyon Difüzyon Problemleri İçin Çoklu Ölçekler Metodu ve Sonlu Fark Metodunun Karşılaştırılması

Güneş¹,

Chianeh²,

Demirbaş³

2020

Gümüşhane Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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In this study, multiple scale method is introduced for singularly perturbed convection-diffusion equation. In this context, the mentioned problem is transformed into partial differential equation. Besides exponentially fitted difference scheme is established by the method of integral identities with using linear basis functions and interpolating quadrature rules with weight functions and remainder term in integral form. Some numerical experiments have been carried out to validate the theoretical results. The main objective of this article is to compare the multiple scale method and finite difference method for singularly perturbed convection-diffusion problems.

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Finite difference scheme for third order singularly perturbed delay differential equation of convection diffusion type with integral boundary condition

Cited by 15 publications

References 9 publications

Numerical treatment of singularly perturbed parabolic partial differential equations with nonlocal boundary condition

Numerical treatment of singularly perturbed parabolic partial differential equations with nonlocal boundary condition

Exponentially fitted numerical method for solving singularly perturbed delay reaction-diffusion problem with nonlocal boundary condition

Singüler Pertürbe Özellikli Konveksiyon Difüzyon Problemleri İçin Çoklu Ölçekler Metodu ve Sonlu Fark Metodunun Karşılaştırılması

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