Parameter optimization for explicit parallel peer two-step methods

Due to a two-step structure certain explicit peer methods with s stages have a natural parallel implementation on s processors. By the peer property all stages have essentially identical properties and we construct a class of zero-stable methods with order p = s in all stages. Two approaches are discussed for choosing the free parameters. In a certain subclass the stability polynomial depends only linearly on a new set of parameters and by employing tailored root locus bounds a linear program can be formulated and solved exactly for stable and accurate methods. The second approach uses Monte-Carlo simulation in a wider class of methods. The two approaches are compared in realistic numerical tests on a parallel computer.