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-v
alue
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.
In this paper, a spline collocation method is developed for finding numerical solutions of general linear eighth-order boundary-value problems (BVPs) and nonlinear eighth-order initial value problems (IVPs). The presented collocation method affords t
he spline solution by the polynomial of degree eleventh which satisfies the BVPs and IVPs at three collocation points. The study shows that the spline collocation method when is applied such this problems is existent and unique. Moreover, the purposed method if applied to these systems will be consistent and the global truncation error equal eleventh.
Numerical results are given for four examples to illustrate the implementation and efficiency of the method. Comparisons of the results obtained by the present method with results obtained by the other methods reveal that the present method is very effective and convenient.
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.
