An equidistributed grid-based second-order scheme for a singularly perturbed Fredholm integro-differential equation with an interior layer

Wubeshet Seyoum Manebo, Mesfin Mekuria Woldaregay, Tekle Gemechu Dinka and Gemechis File Duressa

Applied Mathematics and Computation, 2024, vol. 464, issue C

Abstract: In this study, we introduce and evaluate the effectiveness of the central finite difference coupled with a composite trapezoidal rule on adapted meshes in solving a second-order singularly perturbed Fredholm integro-differential equation with a discontinuous source term. A grid equidistribution technique was employed to address the challenge posed by the perturbation parameter in classical numerical methods. Our approach demonstrated superior precision compared to existing schemes in the literature and achieved second-order uniform convergence.

Keywords: Discontinuous source term; Grid equidistribution; Singular perturbation; Adaptive grid; Uniform convergence; Finite difference scheme; Fredholm integro-differential equation (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:464:y:2024:i:c:s0096300323005672

DOI: 10.1016/j.amc.2023.128398

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