Year: 2021
Author: Wen Yang, Xinyu Cheng, Dong Li, Chaoyu Quan, Wen Yang
Numerical Mathematics: Theory, Methods and Applications, Vol. 14 (2021), Iss. 4 : pp. 1068–1084
Abstract
We consider a parabolic sine-Gordon model with periodic boundary conditions. We prove a fundamental maximum principle which gives a priori uniform control of the solution. In the one-dimensional case we classify all bounded steady states and exhibit some explicit solutions. For the numerical discretization we employ first order IMEX, and second order BDF2 discretization without any additional stabilization term. We rigorously prove the energy stability of the numerical schemes under nearly sharp and quite mild time step constraints. We demonstrate the striking similarity of the parabolic sine-Gordon model with the standard Allen-Cahn equations with double well potentials.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2021-0040
Numerical Mathematics: Theory, Methods and Applications, Vol. 14 (2021), Iss. 4 : pp. 1068–1084
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Sine-Gordon equation backward differentiation formula implicit-explicit scheme.