Parallel Block Predictor–Corrector Methods for Ode's

The problem of achieving parallelism in the solution of the ordinary differential equations is investigated in this paper. The study focuses on an examination of block methods as a practical means for conveniently distributing the computational workload over multiple processors. Both previously suggested and newly proposed predictor-corrector formula pairs are presented and analyzed and a variable stepsize procedure is developed. The performance of two particular members of the block predictor-corrector class is evaluated experimentally using a collection of test problems. A multimicroprocessor system architecture which uses a distributed memory to deal with the interprocessor communications problem is described as a feasible hardware realization of the approach.