A domain decomposition method for solving singularly perturbed parabolic reaction-diffusion problems with time delay

被引:41
|
作者
Singh, Joginder [1 ]
Kumar, Sunil [1 ]
Kumar, Mukesh [2 ]
机构
[1] BHU, Dept Math Sci, Indian Inst Technol, Varanasi 221005, Uttar Pradesh, India
[2] Coll Charleston, Dept Math, Charleston, SC 29424 USA
关键词
delay differential problems; domain decomposition methods; parabolle problems; singular perturbation; uniformly convergent methods; DIFFERENTIAL-DIFFERENCE EQUATIONS; OVERLAPPING SCHWARZ METHOD; FINITE-DIFFERENCE; NUMERICAL-SOLUTION; BOUNDARY-LAYERS; COUPLED SYSTEM;
D O I
10.1002/num.22256
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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 subdornain, 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 epsilon. At the end, some numerical results are given in support of theoretical findings.
引用
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页码:1849 / 1866
页数:18
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