In this paper, the numerical solution of general linear fifth-order boundary-value problem (BVP) is considered. This problem is transformed into three initial value problems (IVPs) and then spline functions with four collocation points are applied to
the three IVPs. The presented spline method enables us to find the spline solution and derivatives up to fifth-order of BVP. By giving four examples and comparing with the other methods, the efficiency and highly accurate of the method will be shown.
In this paper, spline collocation method is considered for solving two forms of problems. The first form is general linear sixth-order boundary-value problem (BVP), and the second form is nonlinear sixth-order initial value problem (IVP). The existen
ce, uniqueness, error estimation and convergence analysis of purpose methods are investigated. The study shows that proposed spline method with three collocation points can find the spline solutions and their derivatives up to sixth-order of the two BVP and IVP, thus is very effective tools in numerically solving such problems. Several examples are given to verify the reliability and efficiency of the proposed method. Comparisons are made to reconfirm the efficiency and accuracy of the suggested techniques.
