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 C2-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 H4/18(6!). Error bounds, in the uniform norm, for ∥s(i)-y(i)∥=O(h4),i=0(1)2, if y∈C6 [0,b], together with illustrative test examples will also be considered.
Original language | English |
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Pages (from-to) | 495-502 |
Number of pages | 8 |
Journal | Journal of Computational and Applied Mathematics |
Volume | 115 |
Issue number | 1-2 |
DOIs | |
Publication status | Published - Mar 1 2000 |
Externally published | Yes |
Keywords
- 56D05
- 65L06
- Absolute stability
- Collocation method
- Periodic stability
- Quintic spline
- Second-order initial value problem
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics