A boundary value technique for singularly perturbed boundary value problem of reactiondiffusion with non-smooth data

In this paper a second-order Singularly Perturbed Ordinary Differential Equation (ODE) of Reaction-Diffusion type Boundary Value Problems (BVPs) with discontinuous source term is considered. A numerical method is suggested in this paper to solve such problems. The domain of definition of the differential equation (a closed interval) is divided into five non-overlapping subintervals, which we call Inner Region (Boundary Layers) and Outer Region. Then, the Differential Equation is solved in these intervals separately. The solutions obtained in this region are combined to give a solution in the entire interval. To obtain terminal boundary conditions (boundary values inside this interval), we mostly use zero-order asymptotic expansion of the solution of the BVPs. Error estimates of the solution and numerical examples are provided.