Solutions of 12th order boundary value problems using non-polynomial spline technique

Non-polynomial spline is used for the numerical solutions of the 12th order linear special case boundary value problems. 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, Int. J. Comput. Math. 78 (1998) 345–362] presented the solutions of 12th 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, near the boundaries of the interval and the results are better in the whole interval. Out of three, two examples compared with that considered by Siddiqi and Twizell (1998), show that the method developed in the paper is more efficient.