Parameter optimization for explicit parallel peer two-step methods
The authors discuss the parameter optimization for explicit parallel peer two-step methods for initial-value problems. Due to a two-step structure certain explicit peer methods with \(s\) stages have a parallel implementation on \(s\) processors. By the peer property all stages have essentially identical properties and the authors constructed 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.
scientific article; zbMATH DE number 5530713