Hypercube Implementation and Performance Analysis for Extrapolation Methods

Solving initial value problems (IVP) for ordinary diierential equations (ODE) has long been believed to be an inherently sequential procedure. But extrapolation methods for solving ODEs which provide solutions of high quality possess a large potential of parallelism. In this article, we present a parallel algorithm for extrapolation based on the explicit Richardson-Euler method. A detailed theoretical runtime analysis using appropriate primitives for communication considers exact runtime, overhead and speedup for a hypercube architecteure. Experiments on the Intel iPSC/860 shows the numerical evidence of the theoretically computed runtimes.