Domain Decomposition Method for Solving Singular Perturbation Problems

Abstract

In this paper, a domain decomposition method for solving singularly perturbed two-point boundary value problems is presented. By using a terminal point, the original problem is divided into inner and outer region problems. An implicit terminal boundary condition at the terminal point is determined. The outer region problem with the implicit boundary condition is solved and produces an explicit boundary condition for the inner region problem. Then, the modified inner region problem (using the stretching transformation) is solved as a two-point boundary value problem. We used fourth order stable central difference method to solve both the inner and outer region problems. The proposed method is iterative on the terminal point. To demonstrate the applicability of the method, we solved several linear and nonlinear singular perturbation problems. Keywords: Singular perturbation problems; finite differences; terminal boundary condition; boundary layer.