Exponential Runge-Kutta method for two-dimensional nonlinear fractional complex Ginzburg-Landau equations

DOI10.1007/s10915-020-01240-xzbMath1442.65340OpenAlexW3034738189WikidataQ115603781 ScholiaQ115603781MaRDI QIDQ2189664

Lu Zhang, Qifeng Zhang, Hai-Wei Sun

Publication date: 16 June 2020

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-020-01240-x

zbMATH Keywords

matrix exponentialToeplitz structureexponential Runge-Kutta methodshift-invert Lanczos methodspace fractional Ginzburg-Landau equation

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Fractional derivatives and integrals (26A33) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22) Preconditioners for iterative methods (65F08) Fractional partial differential equations (35R11) Ginzburg-Landau equations (35Q56)

Related Items (21)

A low-rank Lie-Trotter splitting approach for nonlinear fractional complex Ginzburg-Landau equations ⋮ Second-order maximum principle preserving Strang's splitting schemes for anisotropic fractional Allen-Cahn equations ⋮ High-order conservative scheme for the coupled space fractional nonlinear Schrödinger equations ⋮ A dimensional splitting exponential time differencing scheme for multidimensional fractional Allen-Cahn equations ⋮ A bilateral preconditioning for an L2-type all-at-once system from time-space non-local evolution equations with a weakly singular kernel ⋮ Well-posedness of space fractional Ginzburg-Landau equations involving the fractional Laplacian arising in a Bose-Einstein condensation and its kernel based approximation ⋮ Preconditioned fourth-order exponential integrator for two-dimensional nonlinear fractional Ginzburg-Landau equation ⋮ A conservative difference scheme with optimal pointwise error estimates for two‐dimensional space fractional nonlinear Schrödinger equations ⋮ High‐order finite difference/spectral‐Galerkin approximations for the nonlinear time–space fractional Ginzburg–Landau equation ⋮ Convergence and superconvergence analysis of finite element methods for nonlinear Ginzburg-Landau equation with Caputo derivative ⋮ Numerical study of a fast two-level Strang splitting method for spatial fractional Allen-Cahn equations ⋮ A Fast Two-Level Strang Splitting Method for Multi-Dimensional Spatial Fractional Allen-Cahn Equations with Discrete Maximum Principle ⋮ High-order exponential integrators for the Riesz space-fractional telegraph equation ⋮ High-order numerical algorithm and error analysis for the two-dimensional nonlinear spatial fractional complex Ginzburg-Landau equation ⋮ Fast exponential time differencing/spectral-Galerkin method for the nonlinear fractional Ginzburg-Landau equation with fractional Laplacian in unbounded domain ⋮ Fast iterative solvers for the two-dimensional spatial fractional Ginzburg-Landau equations ⋮ Fast image inpainting strategy based on the space-fractional modified Cahn-Hilliard equations ⋮ Fast numerical schemes for nonlinear space-fractional multidelay reaction-diffusion equations by implicit integration factor methods ⋮ 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 ⋮ A meshless method for solving nonlinear variable-order fractional Ginzburg-Landau equations on arbitrary domains

Uses Software

• mftoolbox

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Higher-order time-stepping methods for time-dependent reaction-diffusion equations arising in biology
• An energy conservative difference scheme for the nonlinear fractional Schrödinger equations
• Crank-Nicolson method for the fractional diffusion equation with the Riesz fractional derivative
• Dynamics of the 3-D fractional complex Ginzburg-Landau equation
• Fourier spectral approximations to the dynamics of 3D fractional complex Ginzburg-Landau equation
• Random attractor for fractional Ginzburg-Landau equation with multiplicative noise
• Exponential time differencing for stiff systems
• Generalized integrating factor methods for stiff PDEs
• Fast numerical solution for fractional diffusion equations by exponential quadrature rule
• An implicit midpoint difference scheme for the fractional Ginzburg-Landau equation
• Algebraic methods for Toeplitz-like matrices and operators
• Fractional quantum mechanics and Lévy path integrals
• An efficient split-step quasi-compact finite difference method for the nonlinear fractional Ginzburg-Landau equations
• RD-rational approximations of the matrix exponential
• Exponential Runge-Kutta methods for parabolic problems.
• An efficient fourth-order in space difference scheme for the nonlinear fractional Ginzburg-Landau equation
• An unconditionally stable linearized difference scheme for the fractional Ginzburg-Landau equation
• Localized numerical impulse solutions in diffuse neural networks modeled by the complex fractional Ginzburg-Landau equation
• Fast iterative solvers and simulation for the space fractional Ginzburg-Landau equations
• A three-level finite difference method with preconditioning technique for two-dimensional nonlinear fractional complex Ginzburg-Landau equations
• On a fractional Ginzburg-Landau equation and 1/2-harmonic maps into spheres
• Uniform convergence of compact and BDF methods for the space fractional semilinear delay reaction-diffusion equations
• Well-posedness for the nonlinear fractional Schrödinger equation and inviscid limit behavior of solution for the fractional Ginzburg-Landau equation
• Galerkin finite element method for the nonlinear fractional Ginzburg-Landau equation
• Fractional generalization of the Ginzburg-Landau equation: an unconventional approach to critical phenomena in complex media
• Shift-invert Lanczos method for the symmetric positive semidefinite Toeplitz matrix exponential
• Exponential integrators
• The world of the complex Ginzburg-Landau equation
• Shift-Invert Arnoldi Approximation to the Toeplitz Matrix Exponential
• Random attractors for the stochastic coupled fractional Ginzburg-Landau equation with additive noise
• Fractional dynamics of coupled oscillators with long-range interaction
• Analysis and Approximation of the Ginzburg–Landau Model of Superconductivity
• Conjugate Gradient Methods for Toeplitz Systems
• Fast exponential time integration scheme for option pricing with jumps
• An efficient difference scheme for the coupled nonlinear fractional Ginzburg–Landau equations with the fractional Laplacian
• A Fourth-order Compact ADI scheme for Two-Dimensional Nonlinear Space Fractional Schrödinger Equation
• Fourth-Order Time-Stepping for Stiff PDEs
• ASYMPTOTIC DYNAMICS OF 2D FRACTIONAL COMPLEX GINZBURG–LANDAU EQUATION
• Fast Exponential Time Integration for Pricing Options in Stochastic Volatility Jump Diffusion Models
• An Introduction to Iterative Toeplitz Solvers
• Functions of Matrices
• Preconditioning Lanczos Approximations to the Matrix Exponential

This page was built for publication: Exponential Runge-Kutta method for two-dimensional nonlinear fractional complex Ginzburg-Landau equations