Preconditioned fourth-order exponential integrator for two-dimensional nonlinear fractional Ginzburg-Landau equation

On τ-preconditioner for a novel fourth-order difference scheme of two-dimensional Riesz space-fractional diffusion equations

(2023) Yuan-Yuan Huang et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

Linearly compact scheme for 2D Sobolev equation with Burgers’ type nonlinearity

(2022) Qifeng Zhang et al.   NUMERICAL ALGORITHMS

The construction of higher-order numerical approximation formula for Riesz derivative and its application to nonlinear fractional differential equations (I)

(2022) Hengfei Ding et al.   Communications in Nonlinear Science and Numerical Simulation

Preconditioners with Symmetrized Techniques for Space Fractional Cahn-Hilliard Equations

(2022) Xin Huang et al.   JOURNAL OF SCIENTIFIC COMPUTING

A τ-preconditioner for a non-symmetric linear system arising from multi-dimensional Riemann-Liouville fractional diffusion equation

(2022) Xue-lei Lin et al.   NUMERICAL ALGORITHMS

Pointwise error estimate in difference setting for the two-dimensional nonlinear fractional complex Ginzburg-Landau equation

(2021) Qifeng Zhang et al.   ADVANCES IN COMPUTATIONAL MATHEMATICS

A Fast Compact Difference Method for Two-Dimensional Nonlinear Space-Fractional Complex Ginzburg-Landau Equations

(2021) global LuZhang   JOURNAL OF COMPUTATIONAL MATHEMATICS

Fast iterative solvers for the two-dimensional spatial fractional Ginzburg–Landau equations

(2021) Min Zhang et al.   APPLIED MATHEMATICS LETTERS

A preconditioner based on sine transform for two-dimensional semi-linear Riesz space fractional diffusion equations in convex domains

(2021) Xin Huang et al.   APPLIED NUMERICAL MATHEMATICS

High-dimensional nonlinear Ginzburg–Landau equation with fractional Laplacian: Discretization and simulations

(2021) Rui Du et al.   Communications in Nonlinear Science and Numerical Simulation

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

(2021) Yong-Liang Zhao et al.   JOURNAL OF COMPUTATIONAL PHYSICS

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

A circulant preconditioner for the Riesz distributed-order space-fractional diffusion equations

(2020) Xin Huang et al.   LINEAR & MULTILINEAR ALGEBRA

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

Fast iterative solvers and simulation for the space fractional Ginzburg–Landau equations

(2019) Min Zhang et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

Error estimate of Fourier pseudo-spectral method for multidimensional nonlinear complex fractional Ginzburg–Landau equations

(2019) Wei Zeng et al.   APPLIED MATHEMATICS LETTERS

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

A fourth-order scheme for space fractional diffusion equations

(2018) Xu Guo et al.   JOURNAL OF COMPUTATIONAL PHYSICS

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

(2018) Dongdong He et al.   NUMERICAL ALGORITHMS

Soliton solutions of fractional complex Ginzburg–Landau equation with Kerr law and non-Kerr law media

(2018) Saima Arshed   OPTIK

Fast and high-order numerical algorithms for the solution of multidimensional nonlinear fractional Ginzburg-Landau equation

(2018) Akbar Mohebbi   European Physical Journal Plus

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

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

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

Fast numerical solution for fractional diffusion equations by exponential quadrature rule

(2015) Lu Zhang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Fourth Order Accurate Scheme for the Space Fractional Diffusion Equations

(2014) Minghua Chen et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Fast Exponential Time Integration for Pricing Options in Stochastic Volatility Jump Diffusion Models

(2014) Hong-Kui Pang et al.   East Asian Journal on Applied Mathematics

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

Using the Restricted-denominator Rational Arnoldi Method for Exponential Integrators

(2011) Paolo Novati   SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS

Shift-invert Lanczos method for the symmetric positive semidefinite Toeplitz matrix exponential

(2010) Hong-Kui Pang et al.   NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS

Shift-Invert Arnoldi Approximation to the Toeplitz Matrix Exponential

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

Exponential integrators

(2010) Marlis Hochbruck et al.   ACTA NUMERICA