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.
Bibliographical noteKAUST Repository Item: Exported on 2021-02-16
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: Supported by the European Research Council under the European Union's Seventh Framework Programme (FP7/2007–2013)/ERC grant agreement no. 291068. The views expressed in this article are not those of the ERC or the European Commission, and the European Union is not liable for any use that may be made of the information contained here.This publication was based on work supported in part by award no. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.