On the lack of convergence of unconditionally stable explicit rational runge-kutta schemes

A. Peirce, J. H. Prevost

Research output: Contribution to journalArticle

Abstract

The poor performance of the rational Runge-Kutta (RRK) schemes of Hairer [2,3] are investigated. By considering two simple model problems, it is demonstrated that this poor performance is in fact due to a lack of convergence. A conceptual model of an unconditionally stable implicit-explicit time-integration scheme is also considered. With the aid of this model, it is possible to establish necessary bounds on the extent of the explicit region for convergence. This demonstrates the limited applicability of such hybrid time-integration schemes.

Original languageEnglish (US)
Pages (from-to)171-180
Number of pages10
JournalComputer Methods in Applied Mechanics and Engineering
Volume57
Issue number2
DOIs
StatePublished - Aug 1986

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications

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