Dissipation-preserving Fourier pseudo-spectral method for the space fractional nonlinear sine–Gordon equation with damping

Fast dissipation-preserving difference scheme for nonlinear generalized wave equations with the integral fractional Laplacian

(2021) Dongdong Hu et al.   Communications in Nonlinear Science and Numerical Simulation

Optimal Regularity and Error Estimates of a Spectral Galerkin Method for Fractional Advection-Diffusion-Reaction Equations

(2020) Zhaopeng Hao et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

TT-M finite element algorithm for a two-dimensional space fractional Gray–Scott model

(2020) Yang Liu et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

Dissipation-preserving Galerkin–Legendre spectral methods for two-dimensional fractional nonlinear wave equations

(2020) Nan Wang et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

A fourth-order dissipation-preserving algorithm with fast implementation for space fractional nonlinear damped wave equations

(2020) Dongdong Hu et al.   Communications in Nonlinear Science and Numerical Simulation

Stable second-order schemes for the space-fractional Cahn–Hilliard and Allen–Cahn equations

(2019) Linlin Bu et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

Accurate numerical methods for two and three dimensional integral fractional Laplacian with applications

(2019) Siwei Duo et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Structure-preserving algorithms for the two-dimensional sine-Gordon equation with Neumann boundary conditions

(2019) Wenjun Cai et al.   JOURNAL OF COMPUTATIONAL PHYSICS

An explicit structure-preserving algorithm for the nonlinear fractional Hamiltonian wave equation

(2019) Yayun Fu et al.   APPLIED MATHEMATICS LETTERS

A pseudo energy-invariant method for relativistic wave equations with Riesz space-fractional derivatives

(2018) J.E. Macías-Díaz et al.   COMPUTER PHYSICS COMMUNICATIONS

On the solution of a Riesz space-fractional nonlinear wave equation through an efficient and energy-invariant scheme

(2018) J. E. Macías-Díaz   INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS

The scalar auxiliary variable (SAV) approach for gradient flows

(2018) Jie Shen et al.   JOURNAL OF COMPUTATIONAL PHYSICS

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

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

A Numerically Efficient Dissipation-Preserving Implicit Method for a Nonlinear Multidimensional Fractional Wave Equation

(2018) Jorge E. Macías-Díaz   JOURNAL OF SCIENTIFIC COMPUTING

Optimal error estimate of a conformal Fourier pseudo-spectral method for the damped nonlinear Schrödinger equation

(2018) Chaolong Jiang et al.   NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS

Solutions of local fractional sine-Gordon equations

(2018) H. Karayer et al.   Waves in Random and Complex Media

A numerically efficient and conservative model for a Riesz space-fractional Klein–Gordon–Zakharov system

(2018) A.S. Hendy et al.   Communications in Nonlinear Science and Numerical Simulation

Direct meshless local Petrov–Galerkin method for the two-dimensional Klein–Gordon equation

(2017) Mohammadreza Ahmadi Darani   ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS

A structure-preserving method for a class of nonlinear dissipative wave equations with Riesz space-fractional derivatives

(2017) J.E. Macías-Díaz   JOURNAL OF COMPUTATIONAL PHYSICS

A conservative Fourier pseudo-spectral method for the nonlinear Schrödinger equation

(2017) Yuezheng Gong et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Numerical Analysis of Fully Discretized Crank–Nicolson Scheme for Fractional-in-Space Allen–Cahn Equations

(2017) Tianliang Hou et al.   JOURNAL OF SCIENTIFIC COMPUTING

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

Analysis and Approximation of a Fractional Cahn--Hilliard Equation

(2017) Mark Ainsworth et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Point-wise error estimate of a conservative difference scheme for the fractional Schrödinger equation

(2016) Pengde Wang et al.   JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

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

(2015) WenYi Tian et al.   MATHEMATICS OF COMPUTATION

Fourier spectral methods for fractional-in-space reaction-diffusion equations

(2014) Alfonso Bueno-Orovio et al.   BIT NUMERICAL MATHEMATICS

Optimal l ∞ error estimates of finite difference methods for the coupled Gross-Pitaevskii equations in high dimensions

(2014) TingChun Wang et al.   Science China-Mathematics

A Crank--Nicolson ADI Spectral Method for a Two-Dimensional Riesz Space Fractional Nonlinear Reaction-Diffusion Equation

(2014) Fanhai Zeng et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

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

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

On the Continuum Limit for Discrete NLS with Long-Range Lattice Interactions

(2012) Kay Kirkpatrick et al.   COMMUNICATIONS IN MATHEMATICAL PHYSICS

Point-wise errors of two conservative difference schemes for the Klein–Gordon–Schrödinger equation

(2012) Tingchun Wang et al.   Communications in Nonlinear Science and Numerical Simulation

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

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