Solutions of twelfth order boundary value problems using thirteen degree spline

Numerical solutions of the twelfth order linear special case boundary value problems are obtained using thirteen degree spline. The end conditions are derived for the definition of spline. Siddiqi and Twizell [S.S. Siddiqi, E.H. Twizell, Spline solutions of linear twelfth-order boundary value problems, J. Comput. Appl. Math. 78 (1997) 371–390] presented the solutions of twelfth order boundary value problems using 12th degree spline, where some unexpected results for the solution and its derivatives were obtained, near the boundaries of the interval. No such situation is observed in this method. The algorithm developed, approximates not only the solution but its higher order derivatives as well. Numerical illustrations are tabulated to demonstrate the practical usefulness of the method.