Numerical search for algebraically stable two-step almost collocation methods

Dajana Conte, Raffaele D'Ambrosio, Zdzislaw Jackiewicz, Beatrice Paternoster

Research output: Contribution to journalArticlepeer-review

31 Scopus citations

Abstract

We investigate algebraic stability of the new class of two-step almost collocation methods for ordinary differential equations. These continuous methods are obtained by relaxing some of the interpolation and collocation conditions to achieve strong stability properties together with uniform order of convergence on the whole interval of integration. We describe the search for algebraically stable methods using the criterion based on the Nyquist stability function proposed recently by Hill. This criterion leads to a minimization problem in one variable which is solved using the subroutine fminsearch from MATLAB. Examples of algebraically stable methods in this class are also presented.

Original languageEnglish (US)
Pages (from-to)304-321
Number of pages18
JournalJournal of Computational and Applied Mathematics
Volume239
Issue number1
DOIs
StatePublished - Feb 1 2013

Keywords

  • A-, L-, and G-stability
  • Algebraic stability
  • Collocation
  • Two-step Runge-Kutta methods

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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