Solving Singular Perturbation Problems by B-Spline and Artificial Viscosity Method

In this paper, we propose a B-spline collocation method using artificial viscosity for solving 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 the scheme comprises a B-spline collocation method, which leads to a tri-diagonal linear system. The design of artificial viscosity parameter is confirmed to be a crucial ingredient for simulating the solution of the problem. A relevant numerical example is also illustrated to demonstrate the accuracy of the method and to verify computationally the theoretical aspects. The result shows that the B-spline method is feasible and efficient and is found to be in good agreement with the exact solution.