A regularized iterative scheme for solving singularly perturbed elliptic PDE

In this paper, we consider a class of singularly perturbed elliptical problems with homogeneous boundary conditions. We propose an iterative method for solving such problems. Convergence analysis and error estimate are derived. The proposed methodology is validated with the numerical results, and is also compared with well-known Shishkin scheme. The study demonstrates that the proposed regularized scheme has an edge over traditional numerical schemes.