Contributed Talk
Fractional-Step Runge-Kutta Methods: Representation and Linear Stability Analysis
University of Saskatchewan, Canada
Abstract
Fractional-step methods are a popular and powerful divide-and-conquer approach for the numerical solution of differential equations. When the integrators of the fractional steps are Runge--Kutta methods, such methods can be written as generalized additive Runge--Kutta (GARK) methods, and thus the representation and analysis of such methods can be done through the GARK framework. We show how the representation and linear stability of such methods are related to the individual integrators and use this framework to explain some common observations in the literature.