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Publication Type : Journal Article
Source : International Journal of Biomathematics, Vol. 12, No. 01, 1950001 (2019).
Url : https://www.worldscientific.com/doi/10.1142/S1793524519500013
Campus : Chennai
School : School of Engineering
Department : Mathematics
Year : 2019
Abstract : In this paper, a class of linear parabolic systems of singularly perturbed second-order differential equations of reaction–diffusion type with initial and Robin boundary conditions is considered. The components of the solution u→ of this system are smooth, whereas the components of ∂u→∂x exhibit parabolic boundary layers. A numerical method composed of a classical finite difference scheme on a piecewise uniform Shishkin mesh is suggested. This method is proved to be first-order convergent in time and essentially first-order convergent in the space variable in the maximum norm uniformly in the perturbation parameters.
Cite this Research Publication : R. Ishwariya, J.J.H. Miller, S. Valarmathi, "A parameter uniform essentially first order convergent numerical method for a parabolic system of singularly perturbed differential equations of reaction-diffusion type with initial and Robin boundary conditions", International Journal of Biomathematics, Vol. 12, No. 01, 1950001 (2019). DOI: https://doi.org/10.1142/S1793524519500013