Quintic C~2-spline integration methods for solving second-order ordinary initial value problems

摘要

In this paper we propose a global collocation method for the integration of the special second-order ordinary initial value problem (IVP) y" = f(x,y). The presented method is based on quintic C~2-splines s(x) as an approximation to the exact solution y(x) of the (IVP). Analysis of stability shows that the method possesses (0,36) ∪ (54,110.2) as interval of periodicity and absolute stability. Moreover, the method has phase-lag of order four with actual phase-lag H~4/18(6!). Error bounds, in the uniform norm, for ||s~((i)) - y~((i))|| = O(h~4), i = 0(1)2, if y ∈ C~6 [0,b], together with illustrative test examples will also be considered.