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In this paper, a class of linear parabolic systems of singularly perturbedsecond order differential equations of reaction-diffusion type with initial andRobin boundary conditions is considered. The components of the solution $\vecu$ of this system exhibit parabolic boundary layers with sublayers. A numericalmethod composed of a classical finite difference scheme on a piecewise uniformShishkin mesh is suggested. This method is proved to be first order convergentin time and essentially first order convergent in the space variable in themaximum norm uniformly in the perturbation parameters

Parameter uniform essentially first order convergence of a fitted mesh  method for a class of parabolic singularly perturbed Robin problem for a  system of reaction-diffusion equations