Spline Method with Three Collocation Parameters for Solving Ninth-Order General Differential Equations Subject to Boundary Conditions

In this paper, we use polynomial splines of eleventh degree with three collocation points to develop a method for computing approximations to the solution and its derivatives up to ninth order for general linear and nonlinear ninth-order boundary-value problems (BVPs). The study shows that the spline method with three collocation points when is applied to these problems is existent and unique. We prove that the proposed method if applied to ninth-order BVPs is stable and consistent of order eleven, and it possesses convergence rate greater than six. Finally, some numerical experiments are presented for illustrating the theoretical results and by comparing the results of our method with the other methods, we reveal that the proposed method is better than others.