High order accuracy nonpolynomial spline solutions for 2 μth order two point boundary value problems

Abstract

Sixth order accurate method based on quintic nonpolynomial spline function for the numerical solution of 2 μth order two point BVPs (where μ is a positive integer) is presented by transforming the problem into a system of μ second order two point BVPs. The nonpolynomial spline function is used to drive some consistency relations for computing approximation to the solution of this problem. The proposed approach gives better approximations than existing polynomial spline and finite difference methods and has a lower computational cost. Convergence analysis of the proposed method is discussed. Numerical examples are included to illustrate the practical usefulness of our method.