B-splines with artificial viscosity for solving singularly perturbed boundary value problems

Abstract

In this paper, we propose a method for the numerical solution of singularly perturbed two-point boundary-value problems (BVPs). The artificial viscosity has been introduced to capture the exponential features of the exact solution on a uniform mesh and then the B-spline collocation method leads to a tridiagonal linear system. The analysis is done on a uniform mesh, which permits its extension to the case of adaptive meshes which may be used to improve the solution. An error estimate for the numerical scheme so constructed is established. The design of an artificial viscosity parameter is confirmed to be a crucial ingredient for simulating the solution of the problem. Known test problems have been studied to demonstrate the accuracy of the method. Results shown by the method are found to be in good agreement with the exact solution.