A fourth-order conservative difference scheme for the Riesz space-fractional sine-Gordon equations and its fast implementation

DOI10.1016/j.apnum.2020.09.009zbMath1459.65161OpenAlexW3088768568WikidataQ112880252 ScholiaQ112880252MaRDI QIDQ2227666

Zhiyong Xing, Liping Wen, Hanyu Xiao

Publication date: 15 February 2021

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2020.09.009

zbMATH Keywords

conservative difference schemesine-Gordon equationRiesz fractional derivativeconvergence and stabilityfast Fourier transform (FFT)

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) KdV equations (Korteweg-de Vries equations) (35Q53) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Numerical methods for discrete and fast Fourier transforms (65T50) Toeplitz, Cauchy, and related matrices (15B05) Fractional partial differential equations (35R11)

Related Items (6)

Numerical analysis of the nonuniform fast L1 formula for nonlinear time-space fractional parabolic equations ⋮ An efficient fourth-order accurate conservative scheme for Riesz space fractional Schrödinger equation with wave operator ⋮ Efficient energy-preserving eighth-order compact finite difference schemes for the sine-Gordon equation ⋮ On \(\tau\)-preconditioner for a novel fourth-order difference scheme of two-dimensional Riesz space-fractional diffusion equations ⋮ An efficient difference scheme for time-fractional KdV equation ⋮ Fast structure-preserving difference algorithm for 2D nonlinear space-fractional wave models

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