ParalleloGAM: A parallel code for ODEs. The method uses the “parallelism across the steps”. It extends a previous paper of the authors [J. Comput. Appl. Math. 78, No. 2, 197-211 (1997; Zbl 0868.65039)] to nonlinear problems and is closely related to a companion paper of L. Brugnano and D. Trigiante [Appl. Numer. Math. 28, No. 1-4, 127-141 (1998; reviewed below)] for the theory. In a first coarse step the grid is determined (only 3 processors active). Then the linear system resulting from the Newton iteration is factored (block diagonal) and solved on p processors. Analysis of operations and numerical tests compared to a sequential Radau code. The parallel version wins only for higher accuracy (many steps).

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