A cubic subdomain Galerkin method over the geometrically graded mesh to the singularly perturbed problem

摘要

In this paper, a subdomain Galerkin method is set up to find solutions of singularly perturbed boundary value problems which are used widely in many areas such as chemical reactor theory, aerodynamics, quantum mechanics, reaction-diffusion process, optimal control, etc. A combination of the cubic B-spline base functions as an approximation function is used to build up the presented method over the geometrically graded mesh. Thus finer mesh can be established through the end parts of the problem domain where steep solutions exist.