Parallel Compound Methods for Solving Partitioned Stiff Systems

Abstract

This paper deals with the solution of partitioned systems of nonlinear stiff differential equations. Given a differential system, the user may specify some equations to be stiff and others to be nonstiff. For the numerical solution of such a system Parallel Compound Methods (PCMs) are studied. Nonstiff equations are integrated by a parallel explicit RK method while a parallel Rosenbrock method is used for the stiff part of the system.
Their order conditions, their convergence and their numerical stability are discussed, and the numerical tests are conducted on a personal computer and a parallel computer.