Nonic spline solutions of eighth order boundary value problems

摘要

Nonic spline is used for the numerical solutions of the eighth order linear special case boundary value problems. The end conditions are derived for the definition of spline. The algorithm developed not only approximates the solutions, but their higher order derivatives as well. The method presented in this paper has also been proved to be second order convergent. Two examples compared with those considered by Inc et al. [M. Inc, D.J. Evans, An efficient approach to approximate solutions of eighth-order boundary-value problems, Int. J. Comput. Math. 81 (6) (2004) 685–692] and Siddiqi et al. [S.S. Siddiqi, E.H. Twizell, Spline solution of linear eighth-order boundary value problems, Comput. Methods Appl. Mech. Eng. 131 (1996) 309–325], show that the method developed in this paper is more efficient.