### SCSC2003 Abstract S6467

#### A New Approach for The Parallel Solution of ODE's Expressed in Symmetric Form

A New Approach for The Parallel Solution of ODE's Expressed in Symmetric Form

Submitting Author: Dr. Osman Abou-Rabia

Abstract:

In this paper, we present a new approach for solving Ordinary Differential Equations (ODE’s) in parallel. The given form of the problem with x as the independent variable is converted into n additional symmetric forms where n is the number of ODE’s. Each of these forms uses one of the state variables as its independent variable. The integration of each of the forms is assigned to a separate processor in a multiprocessor system. We show that for some test problems, different forms demonstrate best performance over different intervals. By continuously switching to the “best” form, we can reach the end of the integration interval in a minimum number of steps.

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