Solving periodic semilinear stiff PDEs in 1D, 2D and 3D with exponential integrators

Hadrien Montanelli and Niall Bootland

Mathematics and Computers in Simulation (MATCOM), 2020, vol. 178, issue C, 307-327

Abstract: 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.

Keywords: Stiff PDEs; Exponential integrators; Fourier spectral methods; Chebfun (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:178:y:2020:i:c:p:307-327

DOI: 10.1016/j.matcom.2020.06.008

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