Parallel predictor-corrector methods for the solution of ordinary differential equations. II

This work presents parallel multistep methods for the solution of ordinary differential equations. The characteristic of parallel computing is that there is a "front" and the computation at points ahead of the front depends only on information behind it. This requires a resetting of serial algorithms and may also lead to numerical errors and instabilities. The analysis of positive and negative aspects of parallel computing is the subject of this paper. Some of the methods presented below are uncommon in the literature on mathematical computing. Others have been elaborated for this study on the basis of the traditional Adams-Bashforth multistep methods. A performance comparison of the methods is made by numerical testing in molecular dynamics calculations. The increase of the number of processors m appears to seriously deteriorate the stability of the calculations and the use of m larger than 2 seems impractical.