Solutions of tenth-order boundary value problems using eleventh degree spline

Abstract

Numerical solutions of the tenth-order linear special case boundary value problems are obtained using eleventh degree spline. The end conditions consistent with the BVP, are also derived. Siddiqi and Twizell [S.S. Siddiqi, E.H. Twizell, Spline solutions of linear tenth order boundary value problems, Int. J. Comput. Math. 68 (1998) 345–362] presented the solutions of tenth-order boundary value problems using tenth degree spline, where some unexpected results for the solution and higher order derivatives were obtained near the boundaries of the interval. No such unexpected situation is observed in this method, near the boundaries of the interval and the results are better in the whole interval. The algorithm developed approximates the solutions, and their higher order derivatives. Numerical illustrations are tabulated to compare the errors with those considered by Siddiqi and Twizell [S.S. Siddiqi, E.H. Twizell, Spline solutions of linear tenth order boundary value problems, Int. J. Comput. Math. 68 (1998) 345–362] and the method is observed to be better.