A second order weighted monotone numerical scheme for time-delayed parabolic initial-boundary-value problem involving a small parameter. (10th June 2022)

• Record Type: Journal Article
• Authors: Das, Abhishek; Govindarao, Lolugu; Mohapatra, Jugal
• Is Part Of: International journal of mathematical modelling and numerical optimisation. Volume 12:Number 3(2022)
• Page Start: 233
• Page End: 251
• Publication Date: 2022-06-10
• Subjects: time delay parabolic problem -- singular perturbation -- boundary layer -- weighted hybrid scheme -- uniform convergence; Mathematical models -- Periodicals; Mathematical optimization -- Periodicals; 519.605
• Languages: English
• ISSNs: 2040-3607

Abstract

In this note, a weighted monotone numerical scheme is proposed to address the time delay (large) parabolic problem which is singularly perturbed in nature. The solution of the problem possesses boundary layer towards the left side of the domain. The initial conditions are given at the present time and also at a past time. The proposed method is based on the Crank-Nicolson scheme in the time scale and a weighted monotone hybrid method for the space derivatives in Shishkin mesh. A rigorous convergence analysis is investigated. The main contribution of this work is to give almost second-order parameter-uniform convergent method. The validity and applicability of the method are preformed by numerical examples, which verify our theoretical claims.