Non-polynomial splines approach to the solution of sixth-order boundary-value problems

Non-polynomial splines, which are equivalent to seven-degree polynomial splines, are used to develop a class of numerical methods for computing approximations to the solution of sixth-order boundary-value problems with two-point boundary conditions. Second-, fourth- and sixth-order convergence is obtained by using standard procedure. It is shown that the present methods give approximations, which are better than those produced by other spline and domain decomposition methods. Numerical examples are given to illustrate practical usefulness of the new approach.