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

Author

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  • Montanelli, Hadrien
  • Bootland, Niall

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.

Suggested Citation

  • Montanelli, Hadrien & Bootland, Niall, 2020. "Solving periodic semilinear stiff PDEs in 1D, 2D and 3D with exponential integrators," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 307-327.
    • Handle: RePEc:eee:matcom:v:178:y:2020:i:c:p:307-327
    DOI: 10.1016/j.matcom.2020.06.008
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    Cited by:

    1. Sungha Yoon & Darae Jeong & Chaeyoung Lee & Hyundong Kim & Sangkwon Kim & Hyun Geun Lee & Junseok Kim, 2020. "Fourier-Spectral Method for the Phase-Field Equations," Mathematics, MDPI, vol. 8(8), pages 1-36, August.
    2. Ham, Seokjun & Kim, Junseok, 2023. "Stability analysis for a maximum principle preserving explicit scheme of the Allen–Cahn equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 453-465.

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