TY - JOUR
T1 - Solving periodic semilinear stiff PDEs in 1D, 2D and 3D with exponential integrators
AU - Montanelli, Hadrien
AU - Bootland, Niall
PY - 2020/12/1
Y1 - 2020/12/1
N2 - Dozens of exponential integration formulas have been proposed for the high-accuracy solution of stiff PDEs such as the Allen–Cahn, Korteweg–de Vries and Ginzburg–Landau equations. We report the results of extensive comparisons in MATLAB and Chebfun of such formulas in 1D, 2D and 3D, focusing on fourth and higher order methods, and periodic semilinear stiff PDEs with constant coefficients. Our conclusion is that it is hard to do much better than one of the simplest of these formulas, the ETDRK4 scheme of Cox and Matthews.
AB - Dozens of exponential integration formulas have been proposed for the high-accuracy solution of stiff PDEs such as the Allen–Cahn, Korteweg–de Vries and Ginzburg–Landau equations. We report the results of extensive comparisons in MATLAB and Chebfun of such formulas in 1D, 2D and 3D, focusing on fourth and higher order methods, and periodic semilinear stiff PDEs with constant coefficients. Our conclusion is that it is hard to do much better than one of the simplest of these formulas, the ETDRK4 scheme of Cox and Matthews.
KW - Chebfun
KW - Exponential integrators
KW - Fourier spectral methods
KW - Stiff PDEs
UR - https://www.sciencedirect.com/journal/mathematics-and-computers-in-simulation
UR - https://arxiv.org/abs/1604.08900v5
U2 - 10.1016/j.matcom.2020.06.008
DO - 10.1016/j.matcom.2020.06.008
M3 - Article
AN - SCOPUS:85087284539
SN - 0378-4754
VL - 178
SP - 307
EP - 327
JO - Mathematics and Computers in Simulation
JF - Mathematics and Computers in Simulation
ER -