Optimal error estimation of two fast structure-preserving algorithms for the Riesz fractional sine-Gordon equation

The primary purpose of this paper is to develop and analyze two fast and conservative algorithms for the fractional sine-Gordon equation. The numerical schemes are derived by using the second-and fourth-order difference method in space and the implicit midpoint rule in time to approximate an equival...

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Bibliographic Details
Published in:Communications in nonlinear science & numerical simulation Vol. 119; p. 107067
Main Authors: Ma, Tingting, Zheng, Qianqian, Fu, Yayun
Format: Journal Article
Language:English
Published: Elsevier B.V 01.05.2023
Subjects:
Fast algorithm
Fractional sine-Gordon equation
Numerical analysis
Structure-preserving
Fractional sine-Gordon equation
Structure-preserving
Numerical analysis
Fast algorithm
ISSN:1007-5704, 1878-7274
Online Access:Get full text
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Summary:The primary purpose of this paper is to develop and analyze two fast and conservative algorithms for the fractional sine-Gordon equation. The numerical schemes are derived by using the second-and fourth-order difference method in space and the implicit midpoint rule in time to approximate an equivalent system obtained via the energy quadratic method. In addition, the conservation, existence and uniqueness, and convergence of the two schemes are investigated. Based on the properties of the Toeplitz matrix, a fast algorithm is given in the calculation for the proposed schemes. Numerical experiments verify the theoretical analysis of the schemes, showing their efficiency and excellent behavior. •We propose the Hamiltonian formulation of the 2D fractional sine-Gordon equation.•Two linearly implicit energy-preserving schemes are developed for the 2D fractional sine-Gordon equation.•An optimal l∞-error estimate for the proposed scheme is established without any restriction on the grid ratio.•A fast algorithm based on the fast Fourier transformation technique is given.
ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2022.107067