Nonpolynomial sextic spline method for the solution along with convergence of linear special case fifth-order two-point boundary value problems

Nonpolynomial sextic spline functions are used to approximate the solution of linear special case fifth-order boundary value problems. Since, presently, the convergence of spline solution of fifth-order boundary value problem is not found in the literature, therefore the convergence of the method is determined which is found to be of fifth order. The convergence of the method is the extension of that developed by Usmani and Sakai [Riaz A. Usmani, Manabu Sakai, Quartic spline solution of the third-order boundary value problems involving third-order differential equations, J. Math. Phys. Sci. 18 (4) (1984) 365–380] for the solution of third-order boundary value problem. The usefulness of the method is illustrated by four examples and confirm the convergence analysis of the method developed.