Sixth Order C 2 -Spline Collocation Method for Integrating Second Order Ordinary Initial Value Problems
Titel:
Sixth Order C 2 -Spline Collocation Method for Integrating Second Order Ordinary Initial Value Problems
Auteur:
Sallam, S. Anwar, M. Naim
Verschenen in:
International journal of computer mathematics
Paginering:
Jaargang 79 (2002) nr. 5 pagina's 625-635
Jaar:
2002
Inhoud:
A new procedure based on sixth degree (Hexic) C 2 -Spline for the numerical integration of the second order initial value problems (IVPs) y^{\prime\prime}=f(x,y) , including those possessing oscillatory solutions, is presented. The proposed method is essentially an implicit sixth order one-step method. Stability analysis shows that the method possesses (0, 75.3)\bigcup (130.2, 201.9) as interval of periodicity and/or absolute stability. In addition, the method has phase-lag (dispersion) of order six with actual phase-lag H^{6}/774144 . Convergence results yield error bounds \parallel\! s^{(r)}-y^{(r)}\!\parallel\,=O\left(h^{6}\right),r=0,1 , in the uniform norm, provided y\in C^{8}[0,b] . Furthermore, it turns out that the method is a continuous extension of a sixth order four-stage Runge-Kutta (-Nystrom) method. Numerical experiments will also be considered.
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