Unconditional energy dissipation and error estimates of the SAV Fourier spectral method for nonlinear fractional generalized wave equation

2021/05/04 by Nan Wang, Meng Li, Wang, Nan +3
Computer Science · Mathematics · Physics and Astronomy · #Applied mathematics #Differential Equations and Numerical Methods #Dissipation #Energy (signal processing) #FOS: Mathematics #Fourier analysis #Fourier transform #Fractional Differential Equations Solutions #Geometry #Lipschitz continuity #Mathematical analysis #Mathematics #Nonlinear Waves and Solitons #Nonlinear system #Numerical Analysis (math.NA) #Physics #Scalar (mathematics) #Spectral method #Wave equation #cs.NA #math.NA

paper · pdf · doi:10.48550/arxiv.2105.01692

published in arXiv (Cornell University) (Cornell University) · 31pages, 9figures

arxiv created 2021/05/04 · openalex publication_date 2021/05/04 · arxiv updated 2021/05/06 · openalex created_date 2021/05/10 · openalex updated_date 2026/08/06

Abstract

In this paper, we consider a second-order scalar auxiliary variable (SAV) Fourier spectral method to solve the nonlinear fractional generalized wave equation. Unconditional energy conservation or dissipation properties of the fully discrete scheme are first established. Next, we utilize the temporal-spatial error splitting argument to obtain unconditional optimal error estimate of the fully discrete scheme, which overcomes time-step restrictions caused by strongly nonlinear system, or the restrictions that the nonlinear term needs to satisfy the assumption of global Lipschitz condition in all previous works for fractional undamped or damped wave equations. Finally, some numerical experiments are presented to confirm our theoretical analysis.

Citations

• Statistical mechanics and dynamics of solvable models with long-range interactions
• Unconditional stability and error estimates of modified characteristics FEMs for the Navier–Stokes equations
• Stability and Error estimates of the SAV Fourier-spectral method for the Phase Field Crystal Equation
• A New Class of Efficient and Robust Energy Stable Schemes for Gradient Flows

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