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