An Efficient Superconvergent Spline Collocation Algorithm for Solving Fourth Order Singularly Perturbed Problems

In this work, improvised quintic B-spline collocation method is used to solve a class of fourth order singularly perturbed boundary value problems. The proposed method is an extension of classical collocation technique. Posteriori corrections are made to quintic B-spline interpolant and its derivatives, which leads to formation of improvised quintic B-spline interpolant. The improvisation is done by forcing the spline interpolant to satisfy interpolatory and some special end conditions. These corrections are made to achieve optimal order of convergence, which is not possible by standard formation of splines. Convergence analysis is performed using Green’s function approach. Four test problems are solved to show the effectiveness of the proposed method and its improvement over classical quintic and septic B-spline collocation techniques. The technique is found to be stable even for extremely small values of perturbation parameter. © 2020, Springer Nature India Private Limited.