Tuesday,
November 4, 12:00 p.m. ECG 317
Raffaele D'Ambrosio
Dept. Math. & Stats
Continuous two-step Runge-Kutta methods for Ordinary Differential Equations
Abstract
We consider the development and analysis of continuous methods for the
numerical solution of ordinary differential equations. The derived methods
belong to the family of two step Runge-Kutta methods (TSRK), introduced by
Jackiewicz and Tracogna in 1995. In particular, we investigate a special
class of continuous TSRK methods based on interpolation and/or collocation
conditions. We consider different approaches to develop continuous TSRK
methods having order p=m (where m is the number of stages) on the whole
integration interval, by relaxing some of these conditions in order to reach
methods with strong stability properties, such as A-stability and
L-stability. We derive families of methods of order up to 4. We also discuss
on the conditions that will guarantee Runge-Kutta stability or quadratic
stability function.
This is a joint work with Z. Jackiewicz.
For further information please contact:
mittelmann@asu.edu