An efficient fourth-order in space difference scheme for the nonlinear fractional Ginzburg-Landau equation
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Publication:1783383
DOI10.1007/s10543-018-0698-9zbMath1412.65095OpenAlexW2793191661MaRDI QIDQ1783383
Publication date: 20 September 2018
Published in: BIT (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10543-018-0698-9
convergenceRiesz fractional derivativeimplicit-explicit methodfractional Ginzburg-Landau equationfractional compact scheme
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) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Fractional partial differential equations (35R11) Ginzburg-Landau equations (35Q56)
Related Items (23)
The construction of higher-order numerical approximation formula for Riesz derivative and its application to nonlinear fractional differential equations (I) ⋮ A Fast Compact Difference Method for Two-Dimensional Nonlinear Space-Fractional Complex Ginzburg-Landau Equations ⋮ Implicit Runge-Kutta and spectral Galerkin methods for the two-dimensional nonlinear Riesz space fractional diffusion equation ⋮ Well-posedness of space fractional Ginzburg-Landau equations involving the fractional Laplacian arising in a Bose-Einstein condensation and its kernel based approximation ⋮ Exponential Runge-Kutta method for two-dimensional nonlinear fractional complex Ginzburg-Landau equations ⋮ Linearized ADI schemes for two-dimensional space-fractional nonlinear Ginzburg-Landau equation ⋮ The construction of an optimal fourth-order fractional-compact-type numerical differential formula of the Riesz derivative and its application ⋮ Fast iterative solvers and simulation for the space fractional Ginzburg-Landau equations ⋮ High-order numerical algorithm and error analysis for the two-dimensional nonlinear spatial fractional complex Ginzburg-Landau equation ⋮ Numerical analysis of a fourth-order linearized difference method for nonlinear time-space fractional Ginzburg-Landau equation ⋮ Fast exponential time differencing/spectral-Galerkin method for the nonlinear fractional Ginzburg-Landau equation with fractional Laplacian in unbounded domain ⋮ A three-level finite difference method with preconditioning technique for two-dimensional nonlinear fractional complex Ginzburg-Landau equations ⋮ High-order compact schemes for semilinear parabolic moving boundary problems ⋮ Fast iterative solvers for the two-dimensional spatial fractional Ginzburg-Landau equations ⋮ Error estimate of Fourier pseudo-spectral method for multidimensional nonlinear complex fractional Ginzburg-Landau equations ⋮ Backward difference formulae and spectral Galerkin methods for the Riesz space fractional diffusion equation ⋮ Uniform convergence of compact and BDF methods for the space fractional semilinear delay reaction-diffusion equations ⋮ A linearized Crank–Nicolson Galerkin FEMs for the nonlinear fractional Ginzburg–Landau equation ⋮ Pointwise error estimate in difference setting for the two-dimensional nonlinear fractional complex Ginzburg-Landau equation ⋮ High-dimensional nonlinear Ginzburg-Landau equation with fractional Laplacian: discretization and simulations ⋮ Space-time finite element method for the distributed-order time fractional reaction diffusion equations ⋮ Numerical solution for multi-dimensional Riesz fractional nonlinear reaction-diffusion equation by exponential Runge-Kutta method ⋮ A fourth-order linearized difference scheme for the coupled space fractional Ginzburg-Landau equation
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