Richardson extrapolation method for solving the Riesz space fractional diffusion problem

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

An extrapolated finite difference method for two-dimensional fractional boundary value problems with non-smooth solution

(2021) Shengyue Li et al.   INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS

A conservative difference scheme with optimal pointwise error estimates for two‐dimensional space fractional nonlinear Schrödinger equations

(2021) Hongling Hu et al.   NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS

Numerical correction of finite difference solution for two-dimensional space-fractional diffusion equations with boundary singularity

(2020) Zhaopeng Hao et al.   NUMERICAL ALGORITHMS

Numerical simulation for the two-dimensional and three-dimensional Riesz space fractional diffusion equations with delay and a nonlinear reaction term

(2018) Shuiping Yang   INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS

An Improved Algorithm Based on Finite Difference Schemes for Fractional Boundary Value Problems with Nonsmooth Solution

(2017) Zhaopeng Hao et al.   JOURNAL OF SCIENTIFIC COMPUTING

Definition of the Riesz derivative and its application to space fractional quantum mechanics

(2016) Selçuk Ş. Bayın   JOURNAL OF MATHEMATICAL 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

Maximum-norm error analysis of a difference scheme for the space fractional CNLS

(2015) Dongling Wang et al.   APPLIED MATHEMATICS AND COMPUTATION

A fourth-order approximation of fractional derivatives with its applications

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

A semi-alternating direction method for a 2-D fractional FitzHugh–Nagumo monodomain model on an approximate irregular domain

(2015) F. Liu et al.   JOURNAL OF COMPUTATIONAL PHYSICS

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

(2015) WenYi Tian et al.   MATHEMATICS OF COMPUTATION

Improved and more feasible numerical methods for Riesz space fractional partial differential equations

(2014) Muhammad Rahman et al.   APPLIED MATHEMATICS AND COMPUTATION

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

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

Stability and convergence of an implicit numerical method for the space and time fractional Bloch-Torrey equation

(2013) Q. Yu et al.   PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES

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

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

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

Maximum norm error bounds of ADI and compact ADI methods for solving parabolic equations

(2008) Hong-Lin Liao et al.   NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS

Anomalous diffusion expressed through fractional order differential operators in the Bloch–Torrey equation

(2007) Richard L. Magin et al.   JOURNAL OF MAGNETIC RESONANCE