 Analysis of a higher order uniformly convergent method for singularly perturbed parabolic delay problemsAmit Sharma and Pratima Rai Applied Mathematics and Computation, 2023, vol. 448, issue C Abstract: We develop and analyze a higher-order uniformly convergent method for time dependent parabolic singularly perturbed convection-diffusion (C-D) problems with space dependent delay. Due to the presence of delay, there occurs an interior layer along with a boundary layer in the solution of the considered problem. A Bakhvalov-Shishkin mesh in space direction and a uniform mesh in time direction is constructed to discretize the domain. Numerical approximation is composed of the classical upwind difference scheme for space variable and the implicit-Euler scheme for time variable. The proposed scheme is proved to have ε-uniform convergence of O(K−1+Δt), where K and Δt denote the number of mesh- intervals in space direction and the step size in time direction, respectively. We further apply the Richardson extrapolation and establish that the resulting scheme has ε-uniform convergence of O(K−2+(Δt)2). Numerical results on two test examples are provided to demonstrate the effectiveness of the scheme. Keywords: Bakhvalov-Shishkin mesh; Upwind finite difference scheme; Richardson extrapolation; Singular perturbation; Delay differential equation (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:448:y:2023:i:c:s0096300323000759 DOI: 10.1016/j.amc.2023.127906 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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