Approximate Solutions of Twelfth-Order Boundary Value Problems by Using Spline Technique
Abstract
In this paper, we develop spline collocation technique for the numerical solution of general twelfth-order linear boundary value problems (BVPs). This technique based on polynomial splines from order sixteenth as well as five collocation points at every subinterval of BVPs. The method developed not only approximates the solution of BVP, but its higher order derivatives as well. We show that the spline collocation method is existent and unique when it is applied into a test problem. Also, its global truncation error is estimated. Moreover, the purposed spline method when applied to test problems will be consistent and convergent from sixteenth order. Three numerical examples are given to illustrate the applicability and efficiency of the new method. Comparisons of our results with some other methods show that our method is very effective and successful.
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