An Improved Extrapolated Collocation Technique for Singularly Perturbed Problems using Cubic B-Spline Functions

In this paper, an improved extrapolated collocation method with cubic B-spline as basis functions is presented. This method is applied to a class of self-adjoint singularly perturbed boundary value problems, with the equispaced discretization of the domain. As with the standard B-spline collocation method, the optimal order of convergence could not be achieved, so posteriori corrections are made in cubic B-spline interpolant and its higher-order derivatives. This results in the enhancement of order of convergence by several powers of step size ‘ $${\hat{h}}$$ ’. The proposed technique has $$O({\hat{h}}^{6})$$ convergence, which is established using Green’s function approach. A number of examples are solved numerically and the results are compared with the results available in the literature to illustrate the efficacy and reliability of the proposed numerical technique.