A connection between quartic spline solution and numerov solution of a boundary value problem

Abstract

This brief paper derives via quartic spline function a new consistency recurrence relation connecting the quartic spline function values at equidistant knots and the corresponding values of the second derivatives. It is shown how this consistency relation may be used in an algorithm for computing quartic spline approximations to the solution and its higher derivatives for a linear two-point boundary value problem. Some numerical evidence is also included to demonstrate the practical usefulness of the algorithm.