Many recent solvers for ordinary differential equations (ODEs) have been designed with an additional potential of method parallelism, but the actual effectiveness of exploiting method parallelism depends on the specific communication and computation requirements induced by the equation to be solved. In this paper we study mixed parallel execution schemes for specific (explicit and implicit) variants of general linear methods, the Parallel Adams-Bashforth methods and the Parallel Adams-Moulton methods, which are new methods providing additional method parallelism. The implementations are realized with a library for multiprocessor task programming. Experiments on a Cray T3E and a dual Xeon cluster show good efficiency results, also for sparse application problems.
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