Numerical investigation of time delay parabolic differential equation involving two small parameters. Issue 6 (20th January 2021)

• Record Type: Journal Article
• Authors: Sahu, Subal Ranjan; Mohapatra, Jugal
• Is Part Of: Engineering computations. Volume 38:Issue 6(2021)
• Page Start: 2882
• Page End: 2899
• Publication Date: 2021-01-20
• Subjects: Time delay -- Uniform convergence -- Hybrid scheme -- Parabolic problem -- Singular perturbation -- Two parameter problem; AMS 65M06 -- 65M12; Computer-aided engineering -- Periodicals; Computer graphics -- Periodicals; 620.00285
• DOI: 10.1108/EC-07-2020-0369
• Languages: English
• ISSNs: 0264-4401

Abstract

Abstract : Purpose: The purpose of this study is to provide a robust numerical method for a two parameter singularly perturbed delay parabolic initial boundary value problem (IBVP). Design/methodology/approach: To solve the problem, the authors have used a hybrid scheme combining the midpoint scheme, the upwind scheme and the second-order central difference scheme for the spatial derivatives. The backward Euler scheme on a uniform mesh is used to approximate the time derivative. Here, the authors have used Shishkin type meshes for spatial discretization. Findings: It is observed that the proposed method converges uniformly with almost second-order spatial accuracy with respect to the discrete maximum norm. Originality/value: This paper deals with the numerical study of a two parameter singularly perturbed delay parabolic IBVP. To solve the problem, the authors have used a hybrid scheme combining the midpoint scheme, the upwind scheme and the second-order central difference scheme for the spatial derivatives. The backward Euler scheme on a uniform mesh is used to approximate the time derivative. The convergence analysis is carried out. It is observed that the proposed method converges uniformly with almost second-order spatial accuracy with respect to the discrete maximum norm. Numerical experiments illustrate the efficiency of the proposed scheme.