Title: A second order weighted monotone numerical scheme for time-delayed parabolic initial-boundary-value problem involving a small parameter

Authors: Abhishek Das; Lolugu Govindarao; Jugal Mohapatra

Addresses: Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, India ' Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Coimbatore, India ' Department of Mathematics, National Institute of Technology Rourkela, 769008, India

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.

Keywords: time delay parabolic problem; singular perturbation; boundary layer; weighted hybrid scheme; uniform convergence.

DOI: 10.1504/IJMMNO.2022.123972

International Journal of Mathematical Modelling and Numerical Optimisation, 2022 Vol.12 No.3, pp.233 - 251

Received: 15 Jun 2021
Accepted: 08 Oct 2021
Published online: 05 Jul 2022 *

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