Evaluation of a family of Runge-Kutta oriented parallel methods for the solution of ODE's.

Abstract

The numerical solution of ordinary differential equations (ODE's) can be a computationally intensive task. It is becoming widely believed that the only feasible means for solving such computationally intensive problems in science and engineering is to use parallel computers efficiently. As a result, there is an increasing interest in the development of parallel methods for the numerical solution of ODE's. This research is, for the most part, still in its preliminary stages. Our goal in this thesis is to contribute to the evolving knowledge about parallel methods for the solution of ODE's. In this context, we examine in detail one particular class of methods. This class is Runge-Kutta oriented in the sense that the underlying computational process is based on Runge-Kutta formulas. However, from a broader perspective, the methods in this family also have an essential predictor-corrector feature. Our study examines stability and performance aspects of this class of methods as originally proposed. In addition, a modification to the approach is suggested and similarly evaluated. Performance is examined in the context of a suite of test problems and results are compared to previously obtained results with two families of parallel Predictor-Corrector oriented methods.