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

S. Sallam, M. Naim Anwar

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

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 languageEnglish
Pages (from-to)495-502
Number of pages8
JournalJournal of Computational and Applied Mathematics
Volume115
Issue number1-2
DOIs
Publication statusPublished - Mar 1 2000
Externally publishedYes

Keywords

  • 56D05
  • 65L06
  • Absolute stability
  • Collocation method
  • Periodic stability
  • Quintic spline
  • Second-order initial value problem

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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