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

Wondimu, Getu Mekonnen; Woldaregay, Mesfin Mekuria; Dinka, Tekle Gemechu; Duressa, Gemechis File

doi:10.3389/fams.2022.1005330

Cited by 4 publications

(2 citation statements)

References 26 publications

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“…In this section, to validate the developed numerical numerical techniques, we solved model examples. As it is tedious to compute the exact solutions of the examples, we apply a variant of the double mesh principle [16,18] as given in Algorithm 1.…”

Section: Numerical Experiments and Discussionmentioning

confidence: 99%

A Fitted Numerical Scheme with Algorithm for Singularly Perturbed Parabolic Partial Differential Equations with Large Negative Shift

Ejere,

Duressa

2023

Preprint

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This research work deals with the formulation of numerical scheme with algorithm to compute singularly perturbed partial differential equations(SP-PDEs) involving a significant negative shift. The problem involves small parameter which causes a rapidly changing boundary layers in the vicinity of a body, and the negative shift term causes interior layer. Such appearance of an abruptly varying layers causes difficulties to find the exact solution and it is not adequate to employ classical numerical methods. The technique presented in this research work simplifies these challenges and yields accurate numerical solution.The stability and convergence analyses of the methods are examined and proven. To test the developed technique, numerical experiments are carried out and confirmed with theoretical analysis.

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Section: Numerical Experiments and Discussionmentioning

confidence: 99%

A Fitted Numerical Scheme with Algorithm for Singularly Perturbed Parabolic Partial Differential Equations with Large Negative Shift

Ejere,

Duressa

2023

Preprint

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“…In [20], the researchers introduced a fitted operator average finite difference method. Wondimu et al [21] developed a numerical method for solving singularly perturbed parabolic partial differential equations with nonlocal boundary condition using non-standard finite difference method for spatial direction and implicit Euler method for temporal direction.…”

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

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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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Numerical scheme for partial differential equations involving small diffusion term with non-local boundary conditions

Bala,

Govindarao,

Das

et al. 2023

J. Appl. Math. Comput.

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

Cited by 4 publications

References 26 publications

A Fitted Numerical Scheme with Algorithm for Singularly Perturbed Parabolic Partial Differential Equations with Large Negative Shift

A Fitted Numerical Scheme with Algorithm for Singularly Perturbed Parabolic Partial Differential Equations with Large Negative Shift

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

Numerical scheme for partial differential equations involving small diffusion term with non-local boundary conditions

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