A parameter uniform almost first order convergent numerical method for non-linear system of singularly perturbed differential equations

In this paper an initial value problem for aВ non-linear system of two singularly perturbed first orderВ differential equations is considered on the interval (0,1].The components of the solution of this system exhibit initialВ layers at 0. A numerical method composed of a classicalВ finite difference scheme on a piecewise uniform ShishkinВ mesh is suggested. This method is proved to be almost firstВ order convergent in the maximum norm uniformly in theВ perturbation parameters.