Parallel ‘Peer’ two-step W-methods and their application to MOL-systems Original Research Article

Parallel two-step W-methods are linearly-implicit integration methods where the s stage values can be computed in parallel. In this paper we consider a new class of two-step W-methods with s peer variables having almost identical characteristics. We discuss different types of such methods with order and stage order s−1 or s and favourable stability properties. The new methods are more robust with respect to stepsize changes since they possess optimal damping at infinity. Numerical comparisons on a shared memory computer show the efficiency of the methods in combination with Krylov-techniques for MOL-systems.