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

Hadrien Montanelli; Niall Bootland

doi:10.1016/j.matcom.2020.06.008

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

Hadrien Montanelli^*
, Niall Bootland

^*Corresponding author for this work

Mathematics And Statistics

Research output: Contribution to journal › Article › peer-review

14 Citations (Scopus)

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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 language	English
Pages (from-to)	307-327
Number of pages	21
Journal	Mathematics and Computers in Simulation
Volume	178
Early online date	23 Jun 2020
DOIs	https://doi.org/10.1016/j.matcom.2020.06.008
Publication status	Published - 1 Dec 2020

Funding

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).

Keywords

Chebfun
Exponential integrators
Fourier spectral methods
Stiff PDEs

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10.1016/j.matcom.2020.06.008

Montanelli-Bootland-MCS-2020-Solving-periodic-semilinear-stiff-PDEs-in-1D-2D-and-3D-with-exponential-integratorsAccepted author manuscript, 539 KBLicence: CC BY-NC-ND 4.0

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

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.",

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author = "Hadrien Montanelli and Niall Bootland",

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doi = "10.1016/j.matcom.2020.06.008",

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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 -

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

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