Strong Stability Preserving General Linear Methods with Runge–Kutta Stability

Giovanna Califano, Giuseppe Izzo, Zdzislaw Jackiewicz

Research output: Contribution to journalArticle

5 Citations (Scopus)

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

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General Linear Methods
Strong Stability
Runge-Kutta
Minimization Problem
Order Conditions
Subroutines
Quadratic programming
Guess
Runge-Kutta Methods
Quadratic Programming
System of Ordinary Differential Equations
Ordinary differential equations
MATLAB
Test Problems
Equality
Numerical Experiment

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

Cite this

Strong Stability Preserving General Linear Methods with Runge–Kutta Stability. / Califano, Giovanna; Izzo, Giuseppe; Jackiewicz, Zdzislaw.

In: Journal of Scientific Computing, 18.01.2018, p. 1-26.

Research output: Contribution to journalArticle

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