A numerical scheme for a weakly coupled system of singularly perturbed delay differential equations on an adaptive mesh. Issue 3 (16th September 2020)

• Record Type: Journal Article
• Authors: Podila, Pramod Chakravarthy; Gupta, Trun; Vigo‐Aguiar, J.
• Is Part Of: Computational and mathematical methods. Volume 3:Issue 3(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2020-09-16
• Subjects: central finite difference scheme -- convection‐diffusion problem -- coupled system -- delay differential equation -- entropy‐like variable -- layer adaptive meshes -- singular perturbation; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Periodicals; Numerical analysis; Mathematics -- Data processing; Periodicals; 004.0151
• DOI: 10.1002/cmm4.1104
• Languages: English
• ISSNs: 2577-7408

Abstract

Summary: In this paper, an adaptive mesh selection strategy is presented for solving a weakly coupled system of singularly perturbed delay differential equations of convection‐diffusion type using second order central finite difference scheme. Layer adaptive mesh is generated via an entropy production operator. The details of the location and width of the boundary layer is not required in the proposed method unlike the popular layer adaptive meshes mainly by Bakhvalov and Shishkin. The method is independent of perturbation parameter and gives us an oscillation‐free solution. The applicability of the proposed method is illustrated by means of three examples.