A low-rank Lie-Trotter splitting approach for nonlinear fractional complex Ginzburg-Landau equations

Exponential Runge–Kutta Method for Two-Dimensional Nonlinear Fractional Complex Ginzburg–Landau Equations

(2020) Lu Zhang et al.   JOURNAL OF SCIENTIFIC COMPUTING

Linearized ADI schemes for two-dimensional space-fractional nonlinear Ginzburg–Landau equation

(2020) Qifeng Zhang et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

Fast exponential time differencing/spectral-Galerkin method for the nonlinear fractional Ginzburg–Landau equation with fractional Laplacian in unbounded domain

(2020) Pengde Wang   APPLIED MATHEMATICS LETTERS

A three-level finite difference method with preconditioning technique for two-dimensional nonlinear fractional complex Ginzburg–Landau equations

(2020) Qifeng Zhang et al.   JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

A relaxation-type Galerkin FEM for nonlinear fractional Schrödinger equations

(2019) Meng Li et al.   NUMERICAL ALGORITHMS

Error Analysis and Numerical Simulations of Strang Splitting Method for Space Fractional Nonlinear Schrödinger Equation

(2019) Shuying Zhai et al.   JOURNAL OF SCIENTIFIC COMPUTING

A linearized Crank–Nicolson Galerkin FEMs for the nonlinear fractional Ginzburg–Landau equation

(2018) Zongbiao Zhang et al.   APPLICABLE ANALYSIS

An efficient split-step quasi-compact finite difference method for the nonlinear fractional Ginzburg–Landau equations

(2018) Nan Wang et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

An unconditionally stable linearized difference scheme for the fractional Ginzburg-Landau equation

(2018) Dongdong He et al.   NUMERICAL ALGORITHMS

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

(2018) Meng Li et al.   NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS

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

Discretized Dynamical Low-Rank Approximation in the Presence of Small Singular Values

(2016) Emil Kieri et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

The Leja Method Revisited: Backward Error Analysis for the Matrix Exponential

(2016) Marco Caliari et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

An energy conservative difference scheme for the nonlinear fractional Schrödinger equations

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

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

A linearly implicit conservative difference scheme for the space fractional coupled nonlinear Schrödinger equations

(2014) Dongling Wang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

A Fourth-order Compact ADI scheme for Two-Dimensional Nonlinear Space Fractional Schrödinger Equation

(2014) Xuan Zhao et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

A projector-splitting integrator for dynamical low-rank approximation

(2013) Christian Lubich et al.   BIT NUMERICAL MATHEMATICS

Dynamical Approximation by Hierarchical Tucker and Tensor-Train Tensors

(2013) Christian Lubich et al.   SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS

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

Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators

(2011) Awad H. Al-Mohy et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Dynamical Tensor Approximation

(2010) Othmar Koch et al.   SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS

Shift-Invert Arnoldi Approximation to the Toeplitz Matrix Exponential

(2010) Spike T. Lee et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Dynamical low-rank approximation: applications and numerical experiments

(2008) Achim Nonnenmacher et al.   MATHEMATICS AND COMPUTERS IN SIMULATION