Abstract : Singularly perturbed partial differential equations occur in many practical problems. These equations are characterized, mathematically, by the presence of a small parameter $\epsilon$ multiplying with one or more of the highest derivatives in a partial differential equation. Finding stable approximate solutions of such problems are mathematically challenging and interesting. Many numerical schemes have been explored in the literature for finding stable approximate solutions of such PDE’s. However, in this talk our attempt is to propose.regularized schemes for finding stable approximate solutions of singularly perturbed PDE’s. We will be discussing theory as well as numerical illustrations for solving singularly perturbed parabolic and elliptic PDE’s.