Spline solutions of linear twelfth-order boundary-value problems

Linear, twelfth-order boundary-value problems (special case) are solved, using polynomial splines of degree 12. 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 solutions, and their higher-order derivatives, of differential equations. merical illustrations are given to show the practical usefulness of the algorithm developed. It is observed that this algorithm is second-order convergent.