Spline solutions of linear eighth-order boundary-value problems

Linear, eighth-order boundary-value problems (special case) are solved, using polynomial splines of degree six. The spline function values at the midknots of the interpolation interval, and the corresponding values of the even-order derivatives are related through consistency relations. The algorithm developed approximates the solution, and their higher-order derivatives, of differential equations. Four numerical illustrations are given to show the practical usefulness of the algorithm developed. It is observed that this algorithm is second-order convergent.