Thursday,
November 18, 12:00 p.m. PSA 311
Angelamaria Cardone
Department of Mathematics and Informatics, University of Salerno
Explicit General Linear Methods with Quadratic Stability
Abstract
The General Linear Methods (GLM) include the standard methods as special case,
but have more free parameters which allow to obtain excellent accuracy and
stability properties. Nevertheless, the derivation of optimal GLM is not a
trivial task, in particular the study of the conditions which guarantee the
best stability properties. Our goal is the construction of methods which
satisfy the Quadratic Stability (QS), i.e. whose stability polynomial has only
two non-zero roots. The QS property simplifies the study of stability and the
search for optimal method parameters. Here we describe the conditions which
guarantee the QS property and the construction of explicit Nordsieck methods
with QS. Finally we compare the absolute stability regions of our methods with
those of explicit Inherent Runge Kutta methods ofi e same order.
