Parallel Two-Step W-Methods with Peer Variables

Abstract

A new class of methods for the solution of stiff initial value problems is introduced that is parallel by design. It has a two-step character and propagates s different "peer" solution variables with essentially identical characteristics from step to step. The main work lies in the solution of s independent linear stage equations which may be solved in parallel. Convergence of order s-1 and stability for general stepsize sequences are proved. Conditions for order s and stronger stability criteria are addressed as well. Promising methods up to order 7 are identified by numerical tests with some widely used stiff test problems. Some of these are competitive with existing software even in sequential computations.