Quintic B-spline method for solving second order linear and nonlinear singularly perturbed two-point boundary value problems

In this paper, we have studied a numerical scheme to solve second order singularly perturbed two-point linear and nonlinear boundary value problems. The boundary layer of this type of problems exhibits at one end (left or right) point of the domain due to the presence of perturbation parameter ε. The quintic B-spline method and suitable piecewise uniform Shishkin mesh have been used. Linear and nonlinear second order singularly perturbed boundary value problems have been solved by the present method. The convergence analysis is also provided and the method is shown to have uniform convergence of fourth order. Numerical results have demonstrated the efficiency of the present method.