L-Stable parallel one-block methods for ordinary differential equations
Résumé
In this contribution, we consider the one-block method designed by W. Couzy, B.P. Sommeijer and P.J. van der Houwen for the purpose of solving ordinary differential equations (ODEs) on a parallel computer. We derive a new set of oder conditions, study the stability and exhibit a new class of parallel methods which are proven to be L-stable up to order seven.