In recent years some attention has been devoted to two-step Runge-Kutta methods (TSRK), in order to achieve classes of methods useful for the numerical solution of real problems. The main topic of this talk is the practical development of TSRK methods for the numerical solution of Ordinary Differential Equations (ODEs). Inspired by recent works on General Linear Methods, we derive the class of TSRK methods with Inherent Quadratic Stability (IQS), i.e. TSRK methods with quadratic stability function, in order to show an algorithmic construction of TSRK methods with strong stability properties. In particular, we deal with the one point spectrum and continuous TSRK with IQS.

Analysis and Practical Construction of Two-Step Runge-Kutta Methods for Ordinary Differential Equations

CONTE, Dajana;D'AMBROSIO, RAFFAELE;
2008

Abstract

In recent years some attention has been devoted to two-step Runge-Kutta methods (TSRK), in order to achieve classes of methods useful for the numerical solution of real problems. The main topic of this talk is the practical development of TSRK methods for the numerical solution of Ordinary Differential Equations (ODEs). Inspired by recent works on General Linear Methods, we derive the class of TSRK methods with Inherent Quadratic Stability (IQS), i.e. TSRK methods with quadratic stability function, in order to show an algorithmic construction of TSRK methods with strong stability properties. In particular, we deal with the one point spectrum and continuous TSRK with IQS.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11386/4505869
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact