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

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) over right arrow of this system are smooth, whereas the components of partial derivative(u) over right arrow/partial derivative 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.