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A domain decomposition method for solving singularly perturbed parabolic reaction‐diffusion problems with time delay
Author(s) -
Singh Joginder,
Kumar Sunil,
Kumar Mukesh
Publication year - 2018
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22256
Subject(s) - mathematics , discretization , backward euler method , singular perturbation , domain decomposition methods , reaction–diffusion system , mathematical analysis , method of matched asymptotic expansions , perturbation (astronomy) , domain (mathematical analysis) , fictitious domain method , parabolic partial differential equation , boundary (topology) , euler method , decomposition method (queueing theory) , euler's formula , boundary value problem , partial differential equation , finite element method , physics , quantum mechanics , thermodynamics , discrete mathematics
We design and analyse a domain decomposition method for solving singularly perturbed parabolic reaction‐diffusion problems with time delay. Using the asymptotic behavior of the solution, we decompose the original domain of the problem into three overlapping subdomains, two of which are boundary layer subdomains and one is a regular subdomain. On each subdomain, we discretize the problem by the backward Euler scheme in the time direction and the central difference scheme in the spatial direction. The proposed method is shown to be uniformly convergent, having almost second order in space and first order in time. In addition, we prove that the proposed method converges much faster for small values of perturbation parameter ε . At the end, some numerical results are given in support of theoretical findings.