Sextic spline solutions of fifth order boundary value problems

The sextic spline is used for numerical solutions of the fifth order linear special case boundary value problems. End conditions for the definition of the spline are derived, consistent with the fifth order boundary value problem. The algorithm developed approximates the solutions, and their higher order derivatives. The method is compared with that developed by Caglar et al. [H.N. Caglar, S.H. Caglar, E.H. Twizell, The numerical solution of fifth-order boundary-value problems with sixth-degree BB-spline functions, Appl. Math. Lett. 12 (1999) 25–30], which is first order convergent, while the method developed in this work is observed to be second order convergent. Two examples are considered for the numerical illustration of the method developed.