A higher order scheme for singularly perturbed delay parabolic turning point problem. Issue 2 (17th July 2020)

• Record Type: Journal Article
• Authors: Yadav, Swati; Rai, Pratima
• Is Part Of: Engineering computations. Volume 38:Issue 2(2021)
• Page Start: 819
• Page End: 851
• Publication Date: 2020-07-17
• Subjects: Hybrid scheme -- Richardson extrapolation -- Shishkin mesh -- Singular perturbed parabolic delay differential equation -- Turning point -- Twin boundary layers; 65M12 -- 65M30 -- 65M06 -- 65M15; Computer-aided engineering -- Periodicals; Computer graphics -- Periodicals; 620.00285
• DOI: 10.1108/EC-03-2020-0172
• Languages: English
• ISSNs: 0264-4401

Abstract

Abstract : Purpose: The purpose of this study is to construct and analyze a parameter uniform higher-order scheme for singularly perturbed delay parabolic problem (SPDPP) of convection-diffusion type with a multiple interior turning point. Design/methodology/approach: The authors construct a higher-order numerical method comprised of a hybrid scheme on a generalized Shishkin mesh in space variable and the implicit Euler method on a uniform mesh in the time variable. The hybrid scheme is a combination of simple upwind scheme and the central difference scheme. Findings: The proposed method has a convergence rate of order O ( N − 2 L 2 + Δ t ) . Further, Richardson extrapolation is used to obtain convergence rate of order two in the time variable. The hybrid scheme accompanied with extrapolation is second-order convergent in time and almost second-order convergent in space up to a logarithmic factor. Originality/value: A class of SPDPPs of convection-diffusion type with a multiple interior turning point is studied in this paper. The exact solution of the considered class of problems exhibit two exponential boundary layers. The theoretical results are supported via conducting numerical experiments. The results obtained using the proposed scheme are also compared with the simple upwind scheme.