A parallel numerical simulation algorithm is presented for fractional-order systems involving Caputo-type derivatives, based on the Adams-Bashforth-Moulton (ABM) predictor-corrector scheme. The parallel algorithm is implemented using several different approaches: a pure MPI version, a combination of MPI with OpenMP optimization and a memory saving speedup approach. All tests run on a BlueGene/P cluster, and comparative improvement results for the running time are provided. As an applied experiment, the solutions of a fractional-order version of a system describing a forced series LCR circuit are numerically computed, depicting cascades of period-doubling bifurcations which lead to the onset of chaotic behavior.
@article{arxiv.1710.01133,
title = {HPC optimal parallel communication algorithm for the simulation of fractional-order systems},
author = {Cosmin Bonchis and Eva Kaslik and Florin Rosu},
journal= {arXiv preprint arXiv:1710.01133},
year = {2017}
}