Third order singularly perturbed delay differential equation of reaction diffusion type with integral boundary condition

Sekar, Elango; Tamilselvan, A.

doi:10.17512/jamcm.2019.2.09

Cited by 10 publications

(8 citation statements)

References 11 publications

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“…□ Thus, we obtained a required ε-uniform error bound. We summarizes the results of this work by considering the semidiscrete error estimate obtained in (13) and (36)and we conclude by the following theorem.…”

Section: Error Analysismentioning

confidence: 69%

“…A FDM with suitable piecewise Shishkin type mesh was developed to solve the problem. The authors in [13] presented a numerical method depends on a FDM on Shishkin mesh to solve the third-order SPDDEs of reaction-diffusion kind with IBC. The authors in [14] used an exponentially fitted numerical scheme to solve SPDDEs of convection-diffusion kind with nonlocal boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

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Hybrid numerical method for solving singularly perturbed partial delay reaction-diffusion problem with integral boundary condition

Wondimu

Duressa

Woldaregay

et al. 2023

Preprint

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In this paper, we study the numerical method for solving singularly perturbed partial delay differential equations with integral boundary conditions. Due to a small perturbation parameter acted on the higher derivative, solution of the problem exhibit a boundary layers at left and right end plane of the domain. An interior layer is also formed because of the presence of large delay on the space variable. A hybrid numerical method is proposed in the spatial direction, and an implicit Euler method is used in temporal direction. The proposed hybrid scheme constitute of cubic spline method in the boundary layer region and a classical finite difference method in the outer layer region. The integral boundary condition is treated using Simpson’s 1/3 rule. The uniform stability and convergence analysis for the proposed scheme is studied. The developed method is uniformly convergent with second-order in space and first-order in time. Two numerical test examples are considered to validate a theoretical result. The numerical results are in agreement with the theoretical estimations. MSC Classification: 65M06 , 65M12 , 65M22 , 65M25

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Section: Error Analysismentioning

confidence: 69%

Section: Introductionmentioning

confidence: 99%

Hybrid numerical method for solving singularly perturbed partial delay reaction-diffusion problem with integral boundary condition

Wondimu

Duressa

Woldaregay

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…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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“…Many different phonemena in science can be modeled by them. They emerge in electrochemistry [22], control theory [7], nuclear engineering [1], fluid dynamics [12] and plasma physics [6] (see, also the references therein).…”

Section: Introductionmentioning

confidence: 99%

A Numerical Method for Solving Singularly Perturbed Quasilinear Boundary Value Problems on Shishkin Mesh

Duru

DEMİRBAŞ

2022

Turkish Journal of Mathematics and Computer Science

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Third order singularly perturbed delay differential equation of reaction diffusion type with integral boundary condition

Cited by 10 publications

References 11 publications

Hybrid numerical method for solving singularly perturbed partial delay reaction-diffusion problem with integral boundary condition

Hybrid numerical method for solving singularly perturbed partial delay reaction-diffusion problem with integral boundary condition

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

A Numerical Method for Solving Singularly Perturbed Quasilinear Boundary Value Problems on Shishkin Mesh

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