Open AccessParameter uniform numerical methods for singularly perturbed delay parabolic differential equations with non-local boundary condition
Author(s) -
Wakjira Tolassa Gobena,
Gemechis File Duressa
Publication year - 2021
Publication title -
international journal of engineering, science and technology andb. lagos
Language(s) - English
Resource type - Journals
ISSN - 2141-2839
DOI - 10.4314/ijest.v13i2.7
Subject(s) - mathematics , mathematical analysis , discretization , boundary value problem , perturbation (astronomy) , backward euler method , singular perturbation , parabolic partial differential equation , uniform convergence , convergence (economics) , partial differential equation , physics , computer science , computer network , bandwidth (computing) , quantum mechanics , economics , economic growth
The motive of this paper is, to develop accurate and parameter uniform numerical method for solving singularly perturbed delay parabolic differential equation with non-local boundary condition exhibiting parabolic boundary layers. Also, the delay term that occurs in the space variable gives rise to interior layer. Fitted operator finite difference method on uniform mesh that uses the procedures of method of line for spatial discretization and backward Euler method for the resulting system of initial value problems in temporal direction is considered. To treat the non-local boundary condition, Simpsons rule is applied. The stability and parameter uniform convergence for the proposed method are proved. To validate the applicability of the scheme, numerical examples are presented and solved for different values of the perturbation parameter. The method is shown to be accurate of O(h2 + △t) . Finally, conclusion of the work is included at the end.