A Crank-Nicolson finite difference scheme for the Riesz space fractional-order parabolic-type sine-Gordon equation

DOI10.1186/S13662-018-1674-ZzbMath1446.65086OpenAlexW2809662331MaRDI QIDQ1712400

Yan Jie Zhou, Zhen-Dong Luo

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/s13662-018-1674-z

zbMATH Keywords

numerical experimentCrank-Nicolson finite difference schemeexistence, stability, and convergenceRiesz space fractional-order parabolic-type sine-Gordon equation

Mathematics Subject Classification ID

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)

Related Items (3)

Fourth-order numerical method for the Riesz space fractional diffusion equation with a nonlinear source term ⋮ A non‐standard finite difference method for space fractional advection–diffusion equation ⋮ An optimized Crank-Nicolson finite difference extrapolating model for the fractional-order parabolic-type sine-Gordon equation

Cites Work

• A reliable treatment of homotopy perturbation method for solving the nonlinear Klein-Gordon equation of arbitrary (fractional) orders
• Exact solutions for the generalized sine-Gordon and the generalized sinh-Gordon equations
• Exact solutions to sine-Gordon-type equations
• Numerical study of the process of nonlinear supratransmission in Riesz space-fractional sine-Gordon equations
• Approximate analytical solution of the coupled sine-Gordon equation using the variational iteration method
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