A Crank-Nicolson linear difference scheme for a BBM equation with a time fractional nonlocal viscous term

DOI10.1186/s13662-018-1815-4zbMath1448.65118OpenAlexW2895447213WikidataQ129137691 ScholiaQ129137691MaRDI QIDQ1716056

Ailing Zhu, Xue Shen

Publication date: 29 January 2019

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

Full work available at URL: https://doi.org/10.1186/s13662-018-1815-4

zbMATH Keywords

stabilityconvergencefinite difference schemeBenjamin-Bona-Mahony (BBM) equationtime-fractional nonlocal viscous term

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

Convergence and stability in maximum norms of linearized fourth-order conservative compact scheme for Benjamin-Bona-Mahony-Burgers' equation ⋮ The splitting Crank-Nicolson scheme with intrinsic parallelism for solving parabolic equations ⋮ The compact finite difference method of two-dimensional Cattaneo model ⋮ Numerical simulation of time fractional BBM-Burger equation using cubic B-spline functions

Cites Work

• Unnamed Item
• Decay of solutions to a viscous asymptotical model for waterwaves: Kakutani-Matsuuchi model
• A new finite difference scheme for the Rosenau-Burgers equation
• Numerical simulation of a solitonic gas in KdV and KdV-BBM equations
• Average implicit linear difference scheme for generalized Rosenau-Burgers equation
• A compact finite difference scheme for the fractional sub-diffusion equations
• A new finite difference scheme for generalized Rosenau-Burgers equation
• Numerical schemes for a model for nonlinear dispersive waves
• Finite difference/spectral approximations to a water wave model with a nonlocal viscous term
• Linearized difference schemes for a BBM equation with a fractional nonlocal viscous term
• The accuracy and stability of an implicit solution method for the fractional diffusion equation
• Numerical simulation for general rosenau-RLW equation: an average linearized conservative scheme
• Efficient numerical schemes for fractional water wave models
• A modified three-level average linear-implicit finite difference method for the Rosenau-Burgers equation
• Crank-Nicolson finite difference scheme for the Rosenau-Burgers equation
• Nonlinear variants of the BBM equation with compact and noncompact physical structures
• The initial-value problem for the Korteweg-de Vries equation
• Long waves on a beach
• Model equations for long waves in nonlinear dispersive systems