A structure preserving difference scheme with fast algorithms for high dimensional nonlinear space-fractional Schrödinger equations

Necessity of introducing non-integer shifted parameters by constructing high accuracy finite difference algorithms for a two-sided space-fractional advection–diffusion model

(2020) Baoli Yin et al.   APPLIED MATHEMATICS LETTERS

Structure-preserving algorithms for the two-dimensional fractional Klein-Gordon-Schrödinger equation

(2020) Yayun Fu et al.   APPLIED NUMERICAL MATHEMATICS

Fast solvers for finite difference scheme of two-dimensional time-space fractional differential equations

(2019) Yun-Chi Huang et al.   NUMERICAL ALGORITHMS

Linearized Crank–Nicolson scheme for the nonlinear time–space fractional Schrödinger equations

(2019) Maohua Ran et al.   JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

Fast conservative numerical algorithm for the coupled fractional Klein-Gordon-Schrödinger equation

(2019) Meng Li et al.   NUMERICAL ALGORITHMS

Symplectic scheme for the Schrödinger equation with fractional Laplacian

(2019) Aiguo Xiao et al.   APPLIED NUMERICAL MATHEMATICS

High-order numerical approximation formulas for Riemann–Liouville (Riesz) tempered fractional derivatives: Construction and application (II)

(2018) Hengfei Ding et al.   APPLIED MATHEMATICS LETTERS

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 algorithm based on TT-M FE system for space fractional Allen–Cahn equations with smooth and non-smooth solutions

(2018) Baoli Yin et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Split-step spectral Galerkin method for the two-dimensional nonlinear space-fractional Schrödinger equation

(2018) Ying Wang et al.   APPLIED NUMERICAL MATHEMATICS

Fast parareal iterations for fractional diffusion equations

(2017) Shu-Lin Wu et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Galerkin-Legendre spectral schemes for nonlinear space fractional Schrödinger equation

(2017) Hui Zhang et al.   NUMERICAL ALGORITHMS

A fast finite volume method for conservative space-fractional diffusion equations in convex domains

(2016) Jinhong Jia et al.   JOURNAL OF COMPUTATIONAL PHYSICS

High-Order Numerical Algorithms for Riesz Derivatives via Constructing New Generating Functions

(2016) Hengfei Ding et al.   JOURNAL OF SCIENTIFIC COMPUTING

Fast Finite Difference Approximation for Identifying Parameters in a Two-dimensional Space-fractional Nonlocal Model with Variable Diffusivity Coefficients

(2016) S. Chen et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

The SCBiCG class of algorithms for complex symmetric linear systems with applications in several electromagnetic model problems

(2015) Xian-Ming Gu et al.   COMPUTER PHYSICS COMMUNICATIONS

An energy conservative difference scheme for the nonlinear fractional Schrödinger equations

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

Fast Numerical Contour Integral Method for Fractional Diffusion Equations

(2015) Hong-Kui Pang et al.   JOURNAL OF SCIENTIFIC COMPUTING

Ground states and concentration phenomena for the fractional Schrödinger equation

(2015) Mouhamed Moustapha Fall et al.   NONLINEARITY

Finite difference method for time-space-fractional Schrödinger equation

(2014) Qun Liu et al.   INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS

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

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

Soliton dynamics for fractional Schrödinger equations

(2013) Simone Secchi et al.   APPLICABLE ANALYSIS

Nonlinear fractional Schrödinger equations in one dimension

(2013) Alexandru D. Ionescu et al.   JOURNAL OF FUNCTIONAL ANALYSIS

Optimal error estimates of finite difference methods for the Gross-Pitaevskii equation with angular momentum rotation

(2012) Weizhu Bao et al.   MATHEMATICS OF COMPUTATION

Positive solutions of the nonlinear Schrödinger equation with the fractional Laplacian

(2012) Patricio Felmer et al.   PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS

A Fast Finite Difference Method for Two-Dimensional Space-Fractional Diffusion Equations

(2012) Hong Wang et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

An Efficient Implicit FEM Scheme for Fractional-in-Space Reaction-Diffusion Equations

(2012) Kevin Burrage et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Global Well-Posedness for the Fractional Nonlinear Schrödinger Equation

(2010) Boling Guo et al.   COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS