An efficient difference scheme for the coupled nonlinear fractional Ginzburg-Landau equations with the fractional Laplacian

Well-posedness of the fractional Ginzburg–Landau equation

(2018) Xian-Ming Gu et al.   APPLICABLE ANALYSIS

A fast linearized conservative finite element method for the strongly coupled nonlinear fractional Schrödinger equations

(2018) Meng Li et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Fast Iterative Method with a Second-Order Implicit Difference Scheme for Time-Space Fractional Convection–Diffusion Equation

(2017) Xian-Ming Gu et al.   JOURNAL OF SCIENTIFIC COMPUTING

Localized numerical impulse solutions in diffuse neural networks modeled by the complex fractional Ginzburg–Landau equation

(2016) Alain Mvogo et al.   Communications in Nonlinear Science and Numerical Simulation

An implicit midpoint difference scheme for the fractional Ginzburg–Landau equation

(2016) Pengde Wang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

A linearized high-order difference scheme for the fractional Ginzburg-Landau equation

(2016) Zhao-peng Hao et al.   NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS

On k-step CSCS-based polynomial preconditioners for Toeplitz linear systems with application to fractional diffusion equations

(2015) Xian-Ming Gu et al.   APPLIED MATHEMATICS LETTERS

Strang-type preconditioners for solving fractional diffusion equations by boundary value methods

(2015) Xian-Ming Gu et al.   JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

A fourth-order approximation of fractional derivatives with its applications

(2015) Zhao-peng Hao et al.   JOURNAL OF COMPUTATIONAL PHYSICS

An energy conservative difference scheme for the nonlinear fractional Schrödinger equations

(2015) Pengde Wang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Random attractors for the stochastic coupled fractional Ginzburg-Landau equation with additive noise

(2015) Ji Shu et al.   JOURNAL OF MATHEMATICAL PHYSICS

A class of second order difference approximations for solving space fractional diffusion equations

(2015) WenYi Tian et al.   MATHEMATICS OF COMPUTATION

Fractional Diffusion on Bounded Domains

(2015) Ozlem Defterli et al.   Fractional Calculus and Applied Analysis

On a Fractional Ginzburg–Landau Equation and 1/2-Harmonic Maps into Spheres

(2014) Vincent Millot et al.   ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS

ASYMPTOTIC DYNAMICS OF 2D FRACTIONAL COMPLEX GINZBURG–LANDAU EQUATION

(2014) HONG LU et al.   INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS

Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints

(2012) Qiang Du et al.   SIAM REVIEW

Well-posedness for the nonlinear fractional Schrödinger equation and inviscid limit behavior of solution for the fractional Ginzburg-Landau equation

(2012) Boling Guo et al.   Fractional Calculus and Applied Analysis

Well-posedness and dynamics for the fractional Ginzburg-Landau equation

(2011) Xueke Pu et al.   APPLICABLE ANALYSIS

Crank–Nicolson method for the fractional diffusion equation with the Riesz fractional derivative

(2011) Cem Çelik et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Numerical methods for fractional partial differential equations with Riesz space fractional derivatives

(2009) Q. Yang et al.   APPLIED MATHEMATICAL MODELLING

Difference methods for computing the Ginzburg-Landau equation in two dimensions

(2009) Qiubin Xu et al.   NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS

Numerical Methods for the Variable-Order Fractional Advection-Diffusion Equation with a Nonlinear Source Term

(2009) P. Zhuang et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS