Strong Stability Preserving General Linear Methods with Runge–Kutta Stability

Giovanna Califano, Giuseppe Izzo, Zdzislaw Jackiewicz

Research output: Contribution to journalArticle

7 Scopus citations

Abstract

We investigate strong stability preserving (SSP) general linear methods (GLMs) for systems of ordinary differential equations. Such methods are obtained by the solution of the minimization problems with nonlinear inequality constrains, corresponding to the SSP property of these methods, and equality constrains, corresponding to order and stage order conditions. These minimization problems were solved by the sequential quadratic programming algorithm implemented in MATLAB(Formula presented.) subroutine fmincon.m starting with many random guesses. Examples of transformed SSP GLMs of order (Formula presented.), and 4, and stage order (Formula presented.) have been determined, and suitable starting and finishing procedures have been constructed. The numerical experiments performed on a set of test problems have shown that transformed SSP GLMs constructed in this paper are more accurate than transformed SSP DIMSIMs and SSP Runge–Kutta methods of the same order.

Original languageEnglish (US)
Pages (from-to)1-26
Number of pages26
JournalJournal of Scientific Computing
DOIs
StateAccepted/In press - Jan 18 2018

Keywords

  • Construction of SSP methods
  • General linear methods
  • Inherent Runge–Kutta stability
  • Order conditions
  • Runge–Kutta stability
  • Strong stability preserving (SSP) methods

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Engineering(all)
  • Computational Theory and Mathematics

Fingerprint Dive into the research topics of 'Strong Stability Preserving General Linear Methods with Runge–Kutta Stability'. Together they form a unique fingerprint.

Cite this