Quintic C2-spline integration methods for solving second-order ordinary initial value problems

Abstract

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.