Parallel computing on Lyapunov exponents for continuous parameter-dependent ordinary differential equations

The paper concerns the parallel computing and its application for solving the full Lyapunov exponents in the general nonlinear parameter-dependent continuous ordinary differential equations. Based on a standard serial algorithm developed by Wolf et al. (1985), we present a parallel algorithm using the block-cyclic decomposition method, and then apply it for solving the Lyapunov exponents of a continuous differential equation. By testing its performance of the parallel algorithm on the supercomputer DAWNING-200011, it is proved that the parallel algorithm is of high level parallelism, no need for message passing (little communication cost), and little I/O. In addition, the algorithm can be extended to any high dimensional ordinary differential equations.