Implementation of the Runge-Kutta-Fehlberg Method for Solution of Ordinary Differential Equations on a Parallel Processor

摘要

A recent advance in computer architecture, the parallel processor computer, has made it theoretically feasible to reduce the time required to integrate a system of n ordinary differential equations by a factor of n. One established numerical technique, the Runge-Kutta-Fehlberg method, is adapted for parallel processing on an Intel Scientific Computer iPSC Concurrent Supercomputer. The algorithm is evaluated using a standardized collection of systems of equations. It is concluded that this type of parallel processor is not suited for the solution of this problem due to the communications overhead required. Short developments of ordinary differential equations and numerical integration methods are provided as background. (Author)