A sixth order optimal B-spline collocation method for solving Bratu’s problem

Abstract

In this paper, we describe an optimal B-spline collocation method to solve one-dimensional non-linear Bratu problem. Convergence result of the method is established through Green’s function technique and it is proved that the method has sixth order convergence. The applicability and accuracy of the method are demonstrated through two numerical examples. It is shown that the computational result is consistent with theoretical prediction. Moreover, the numerical results obtained by the present method are compared with those obtained by two other B-spline collocation approaches reported in the literature. The computed results reveal that our method is accurate and easy to implement.