Non-polynomial cubic spline discretization for system of non-linear singular boundary value problems using variable mesh

Abstract

In this paper, we propose two generalized non-polynomial cubic spline schemes using a variable mesh to solve the system of non-linear singular two point boundary value problems. Theoretical analysis proves that the proposed methods have second- and third-order convergence. Both methods are applicable to singular boundary value problems. Numerical results are also provided to show the accuracy and efficiency of the proposed methods.