A conservative difference scheme for the Riesz space-fractional sine-Gordon equation

DOI10.1186/s13662-018-1689-5zbMath1446.65094OpenAlexW2850841886MaRDI QIDQ1712443

Liping Wen, Zhiyong Xing

Publication date: 22 January 2019

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13662-018-1689-5

zbMATH Keywords

conservation lawNewton methodRiesz fractional derivativeconvergence and stabilityspace-fractional sine-Gordon equation

Mathematics Subject Classification ID

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) Soliton equations (35Q51) Fractional partial differential equations (35R11)

Related Items (10)

A nonlinear discrete model for approximating a conservative multi-fractional Zakharov system: analysis and computational simulations ⋮ Two efficient spectral methods for the nonlinear fractional wave equation in unbounded domain ⋮ A fourth-order conservative difference scheme for the Riesz space-fractional sine-Gordon equations and its fast implementation ⋮ On the dissipativity of some Caputo time-fractional subdiffusion models in multiple dimensions: theoretical and numerical investigations ⋮ A Linearized Difference Scheme for Time-Fractional Sine-Gordon Equation ⋮ A dissipation-preserving finite element method for nonlinear fractional wave equations on irregular convex domains ⋮ An explicit fourth-order energy-preserving difference scheme for the Riesz space-fractional sine-Gordon equations ⋮ Theoretical analysis of an explicit energy-conserving scheme for a fractional Klein-Gordon-Zakharov system ⋮ On a nonlinear energy-conserving scalar auxiliary variable (SAV) model for Riesz space-fractional hyperbolic equations ⋮ Unconditional energy dissipation and error estimates of the SAV Fourier spectral method for nonlinear fractional generalized wave equation

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