Quintic nonpolynomial spline method for the solution of a second-order boundary-value problem with engineering applications

Nonpolynomial quintic spline functions are used to develop a numerical algorithm for computing an approximation to the solution of a system of second order boundary value problems associated with heat transfer. We show that the approximate solutions obtained by our algorithm are better than those produced by other spline and domain decomposition methods. A comparison of our algorithm with nonpolynomial quadratic spline method is discussed with the help of two numerical examples.