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

✍ Scribed by S. Sallam; M.Naim Anwar

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 88 KB
• Volume: 115
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/s0377-0427(99)00174-0

✦ Synopsis

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.