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A Structure-Preserving Finite Difference Scheme for the Nonlinear Space Fractional Sine-Gordon Equation with Damping Based on the T-SAV Approach
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A Structure-Preserving Finite Difference Scheme for the Nonlinear Space Fractional Sine-Gordon Equation with Damping Based on the T-SAV Approach
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A Structure-Preserving Finite Difference Scheme for the Nonlinear Space Fractional Sine-Gordon Equation with Damping Based on the T-SAV Approach
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Journal Article
A Structure-Preserving Finite Difference Scheme for the Nonlinear Space Fractional Sine-Gordon Equation with Damping Based on the T-SAV Approach
2025
Overview
This paper presents a high-order structure-preserving difference scheme for the nonlinear space fractional sine-Gordon equation with damping, employing the triangular scalar auxiliary variable approach. The original equation is reformulated into an equivalent system that satisfies a modified energy conservation or dissipation law, significantly reducing the computational complexity of nonlinear terms. Temporal discretization is achieved using a second-order difference method, while spatial discretization utilizes a simple and easily implementable discrete approximation for the fractional Laplacian operator. The boundedness and convergence of the proposed numerical scheme under the maximum norm are rigorously analyzed, demonstrating its adherence to discrete energy conservation or dissipation laws. Numerical experiments validate the scheme’s effectiveness, structure-preserving properties, and capability for long-time simulations for both one- and two-dimensional problems. Additionally, the impact of the parameter ε on error dynamics is investigated.
Publisher
MDPI AG
