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Journal of Applied Mathematics and Computing

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01.10.2022 | Original Research

A uniformly convergent defect correction method for parabolic singular perturbation problems with a large delay

verfasst von: Monika Choudhary, Aditya Kaushik

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 2/2023

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Abstract

This paper presents a study of singularly perturbed parabolic convection–diffusion problems with delay. The solution of the problem exhibits a weak interior layer and a strong boundary layer. In these layers, the physical variable changes rapidly over small domains in space and in a short time interval. The solution reveals a multiscale character, which adds stiffness to the problem. We present a second-order accurate difference approximation based on the defect correction method to capture this multiscale phenomenon. The problem is discretized by an implicit Euler scheme in time variable on a uniform mesh and a defect correction method consisting of the upwind scheme and the central difference scheme in space variable on a layer-adapted mesh in such a way that it captures the interior as well as the boundary layers. The proposed method is not only free from directional bias but unconditionally stable and converges uniformly. Test examples and numerical results verify the theoretical predictions and illustrate the efficiency of the method.

Vorheriger Artikel Qualitative analysis of second-order fuzzy difference equation with quadratic term

Nächster Artikel Convergence rate analysis of an extrapolated proximal difference-of-convex algorithm

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Titel: A uniformly convergent defect correction method for parabolic singular perturbation problems with a large delay
verfasst von: Monika Choudhary
Aditya Kaushik
Publikationsdatum: 01.10.2022
Verlag: Springer Berlin Heidelberg
Erschienen in: Journal of Applied Mathematics and Computing / Ausgabe 2/2023
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-022-01796-x

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