A tension spline fitted numerical scheme for singularly perturbed reaction-diffusion problem with negative shift.

Ababi Hailu Ejere, Tekle Gemechu Dinka, Mesfin Mekuria Woldaregay, Gemechis File Duressa

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Article in BMC research notes, 2023. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.

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4 authors.

Ababi Hailu EjereDepartment of Applied Mathematics, Adama Science and Technology University, Adama, Ethiopia. hailu_ababi@yahoo.com.ORCID https://orcid.org/0000-0002-9171-2796

Tekle Gemechu DinkaDepartment of Applied Mathematics, Adama Science and Technology University, Adama, Ethiopia.ORCID https://orcid.org/0000-0003-0592-9508

Mesfin Mekuria WoldaregayDepartment of Applied Mathematics, Adama Science and Technology University, Adama, Ethiopia.ORCID https://orcid.org/0000-0002-6555-7534

Gemechis File DuressaDepartment of Mathematics, Jimma University, Jimma, Ethiopia.ORCID https://orcid.org/0000-0003-1889-4690

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6 · The paper itself

Abstract

objectiveThe paper is focused on developing and analyzing a uniformly convergent numerical scheme for a singularly perturbed reaction-diffusion problem with a negative shift. The solution of such problem exhibits strong boundary layers at the two ends of the domain due to the influence of the perturbation parameter, and the term with negative shift causes interior layer. The rapidly changing behavior of the solution in the layers brings significant difficulties in solving the problem analytically. We have treated the problem by proposing a numerical scheme using the implicit Euler method in the temporal direction and a fitted tension spline method in the spatial direction with uniform meshes.

resultStability and uniform error estimates are investigated for the developed numerical scheme. The theoretical finding is demonstrated by numerical examples. It is obtained that the developed numerical scheme is uniformly convergent of order one in time and order two in space.

Indexed as

DiffusionBoundary layersSingularly perturbed problemTension spline methodUniform convergence

Identifiers

PMID37349785

DOI10.1186/s13104-023-06361-8

PMCPMC10286455

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