A parameter uniform difference scheme for singularly perturbed parabolic delay differential equation with Robin type boundary condition

P. Avudai Selvi and N. Ramanujam

Applied Mathematics and Computation, 2017, vol. 296, issue C, 101-115

Abstract: A Robin type boundary value problem for a singularly perturbed parabolic delay differential equation is studied on a rectangular domain in the x - t plane. The second-order space derivative is multiplied by a small parameter, which gives rise to parabolic boundary layers on the two lateral sides of the rectangle. A numerical method comprising a standard finite difference scheme on a rectangular piecewise uniform fitted mesh of Nx × Nt elements condensing in the boundary layers is suggested and it is proved to be parameter-uniform. More specifically, it is shown that the errors are bounded in the maximum norm by C(Nx−2ln2Nx+Nt−1), where C is a constant independent of Nx, Nt and the small parameter. To validate the theoretical result an example is provided.

Keywords: Parabolic differential equations; Delay; Singularly perturbed problem; Finite difference scheme; Shishkin mesh (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:296:y:2017:i:c:p:101-115

DOI: 10.1016/j.amc.2016.10.027

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