THE USE OF QUARTIC SPLINES IN THE NUMERICAL-SOLUTION OF A 4TH-ORDER BOUNDARY-VALUE PROBLEM

This paper derives via uniform quartic polynomial splines a few new consistency relations connecting the quartic spline function values at midknots and the corresponding values of the second and fourth derivatives, respectively. It is shown how these relations may be used in an algorithm for computing approximations to the solution and its higher derivatives for a linear fourth-order boundary value problem. Two numerical illustrations are also included to demonstrate the practical usefulness of our algorithm.