An optimal Quintic B-spline collocation method for fourth-order singular singularly perturbed problems

Abstract

A collocation method with optimal quintic B-spline as basis functions is used to solve the fourth-order singular singularly perturbed boundary value problems(SSP BVPs). In this work, posteriori corrections are made in second and higher-order derivatives of quintic B-spline interpolant. This results in the enhancement of the order of convergence up to $O(h^{6})$. Suitable examples are solved to show the effectiveness of the method and improvement in the results as compared to existing work. Also, the order of convergence is calculated numerically which agrees with the theoretical results.