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

Hadrien Montanelli, Niall Bootland

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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.

Original languageEnglish
Pages (from-to)307-327
Number of pages21
JournalMathematics and Computers in Simulation
Volume178
Early online date23 Jun 2020
DOIs
Publication statusE-pub ahead of print - 23 Jun 2020

Keywords

  • Chebfun
  • Exponential integrators
  • Fourier spectral methods
  • Stiff PDEs

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