A Sixth-Order Numerical Method Based on Shishkin Mesh for Singularly Perturbed Boundary Value Problems

Recently, Lodhi and Mishra (J Comput Appl Math 319:170-187, 2017) presented the standard B-spline method based on quintic B-spline basis functions to solve a type of singularly perturbed boundary value problems (SPBVP). We note that their method provides only fourth-order convergence approximation to the solution of such problem. In this paper, we present a novel optimal B-spline technique, based on same quintic B-spline basis function as used in Lodhi and Mishra (2017), for solving linear and nonlinear SPBVP. The advantage of the suggested method over the method in Lodhi and Mishra (2017) is that our method has sixth-order rate of convergence. To obtain higher order of convergence, a high-order perturbation of the SPBVP is generated. The method is tested for its efficiency by applying it on five test problems.