Polynomial and nonpolynomial spline approaches to the numerical solution of second order boundary value problems

In this paper, quadratic and cubic polynomial and nonpolynomial spline functions based methods are presented to find approximate solutions to second order boundary value problems. Using these spline functions we drive a few consistency relations which to be used for computing approximations to the solution for second order boundary value problems. The present approaches have less computational cost. Convergence analysis of these methods is discussed. Two numerical examples are included to illustrate the practical usefulness of the proposed methods.