Design, analysis and testing of some parallel two-step W-methods for stiff systems Original Research Article

Parallel two-step W-methods are linearly-implicit integration methods where the s stage values can be computed in parallel. We construct methods of stage order q=s and order p=s with favourable stability properties. Generalizations for the concepts of A- and L-stability are proposed and conditions for stiff accuracy are given. Numerical comparisons on a shared memory computer show the efficiency of the methods, especially in combination with Krylov-techniques for large stiff systems.