Computational and Applied Math Proseminar

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