A Parallel Spectral Element Method for Fractional Lorenz System

We provide a parallel spectral element method for the fractional Lorenz system numerically. The detailed construction and implementation of the method are presented. Thanks to the spectral accuracy of the presented method, the storage requirement due to the “global time dependence” can be considerably relaxed. Also, the parareal method combining spectral element method reduces the computing time greatly. Finally, we have tested the chaotic behaviors of fractional Lorenz system. Our numerical results are in excellent agreement with the results from other numerical methods.