Three Point Spline Collocation Method for Solving General Linear and Nonlinear Eighth-Order Boundary-Value Problems

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 the 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.