ETDRK4

This repository contains a Python implementation of ETDRK4 (Exponential Time Differencing fourth-order Runge-Kutta) [1] method for solving stiff nonlinear PDEs.

In particular both PyTorch and Numpy implementations for the Kuramoto-Sivashinsky equation are provided, ported from the MATLAB code proposed by Aly-Khan Kassam and Lloyd N. Trefethen in "Fourth-Order Time-Stepping for Stiff PDEs".

Citations

[1] @article{doi:10.1137/S1064827502410633,
        author = {Kassam, Aly-Khan and Trefethen, Lloyd N.},
        title = {Fourth-Order Time-Stepping for Stiff PDEs},
        journal = {SIAM Journal on Scientific Computing},
        volume = {26},
        number = {4},
        pages = {1214-1233},
        year = {2005},
        doi = {10.1137/S1064827502410633},
        URL = {https://doi.org/10.1137/S1064827502410633},
        eprint = {https://doi.org/10.1137/S1064827502410633}
    }