Open AccessFitted numerical scheme for singularly perturbed convection-diffusion reaction problems involving delays
Author(s) -
Mesfin Mekuria Woldaregay,
Worku Tilahun Aniley,
Gemechis File Duressa
Publication year - 2021
Publication title -
theoretical and applied mechanics/theoretical and applied mechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.279
H-Index - 6
eISSN - 2406-0925
pISSN - 1450-5584
DOI - 10.2298/tam201208006w
Subject(s) - mathematics , convergence (economics) , mathematical analysis , series (stratigraphy) , boundary value problem , boundary (topology) , stability (learning theory) , domain (mathematical analysis) , delay differential equation , diffusion , scheme (mathematics) , singular perturbation , convection–diffusion equation , exponential function , reaction–diffusion system , differential equation , physics , computer science , paleontology , machine learning , economics , biology , economic growth , thermodynamics
This paper deals with solution methods for singularly perturbed delay differential equations having delay on the convection and reaction terms. The considered problem exhibits an exponential boundary layer on the left or right side of the domain. The terms with the delay are treated using Taylor?s series approximation and the resulting singularly perturbed boundary value problem is solved using a specially designed exponentially finite difference method. The stability of the scheme is analysed and investigated using a comparison principle and solution bound. The formulated scheme converges uniformly with linear order of convergence. The theoretical findings are validated using three numerical test examples.