Sixth order C2-spline collocation method for integrating second order ordinary initial value problems

S. Sallam, M. Naim Anwar

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)

Abstract

A new procedure based on sixth degree (Hexic) C2-Spline for the numerical integration of the second order initial value problems (IVPs) y″ = 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)∪(030.2, 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 ∥ s (r) - y(r) ∥= O(h6), r = 0, 1, in the uniform norm, provided y ∈ C8[0, b]. Furthermore, it turns out that the method is a continuous extension of a sixth order four-stage Runge-Kutta (-Nyström) method. Numerical experiments will also be considered.

Original languageEnglish
Pages (from-to)625-635
Number of pages11
JournalInternational Journal of Computer Mathematics
Volume79
Issue number5
DOIs
Publication statusPublished - 2002

Keywords

  • Absolute stability, Periodic stability, Oscillatory solutions
  • Collocation methods
  • Second-order initial value problems
  • Sixth degree splines

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Theory and Mathematics
  • Applied Mathematics

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