Exponential spline solutions for a class of two point boundary value problems over a semi-infinite range

In this paper, we developed numerical methods of order O(h ²) and O(h ⁴) based on exponential spline function for the numerical solution of class of two point boundary value problems over a Semi-infinite range. The present approach gives better approximations over all the existing finite difference methods. Properties of the infinite linear system are established. Convergence analysis and a bound on the approximate solution are discussed. Test problem with various kinds of boundary conditions is included to illustrate the practical usefulness and superiority of our methods.