Energy-conserving and time-stepping-varying ESAV-Hermite-Galerkin spectral scheme for nonlocal Klein-Gordon-Schrödinger system with fractional Laplacian in unbounded domains

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

(2020) Yayun Fu et al.   APPLIED NUMERICAL MATHEMATICS

Semi-implicit Hermite–Galerkin Spectral Method for Distributed-Order Fractional-in-Space Nonlinear Reaction–Diffusion Equations in Multidimensional Unbounded Domains

(2020) Shimin Guo et al.   JOURNAL OF SCIENTIFIC COMPUTING

High-order structure-preserving algorithms for the multi-dimensional fractional nonlinear Schrödinger equation based on the SAV approach

(2020) Yayun Fu et al.   MATHEMATICS AND COMPUTERS IN SIMULATION

A Second Order BDF Numerical Scheme with Variable Steps for the Cahn--Hilliard Equation

(2019) Wenbin Chen et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

A linear, symmetric and energy-conservative scheme for the space-fractional Klein–Gordon–Schrödinger equations

(2019) Ying Wang et al.   APPLIED MATHEMATICS LETTERS

What is the fractional Laplacian? A comparative review with new results

(2019) Anna Lischke et al.   JOURNAL OF COMPUTATIONAL PHYSICS

The scalar auxiliary variable (SAV) approach for gradient flows

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

A New Class of Semi-Implicit Methods with Linear Complexity for Nonlinear Fractional Differential Equations

(2018) Fanhai Zeng et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Fractional spectral and pseudo-spectral methods in unbounded domains: Theory and applications

(2017) Hassan Khosravian-Arab et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Smoothing for the Zakharov and Klein--Gordon--Schrödinger Systems on Euclidean Spaces

(2017) E. Compaan   SIAM JOURNAL ON MATHEMATICAL ANALYSIS

Hermite Spectral Methods for Fractional PDEs in Unbounded Domains

(2017) Zhiping Mao et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Global well-posedness of the fractional Klein-Gordon-Schrödinger system with rough initial data

(2016) ChunYan Huang et al.   Science China-Mathematics

Fractional Sturm–Liouville boundary value problems in unbounded domains: Theory and applications

(2015) Hassan Khosravian-Arab et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Fractional quantum mechanics in polariton condensates with velocity-dependent mass

(2015) F. Pinsker et al.   PHYSICAL REVIEW B

Fractional quantum mechanics on networks: Long-range dynamics and quantum transport

(2015) A. P. Riascos et al.   PHYSICAL REVIEW E

Provably unconditionally stable, second-order time-accurate, mixed variational methods for phase-field models

(2011) Hector Gomez et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Observation of bright polariton solitons in a semiconductor microcavity

(2011) M. Sich et al.   Nature Photonics

An Adaptive Time-Stepping Strategy for the Molecular Beam Epitaxy Models

(2011) Zhonghua Qiao et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

On the nonlocality of the fractional Schrödinger equation

(2010) M. Jeng et al.   JOURNAL OF MATHEMATICAL PHYSICS

Singular Limits of Klein–Gordon–Schrödinger Equations to Schrödinger–Yukawa Equations

(2010) Weizhu Bao et al.   MULTISCALE MODELING & SIMULATION

Explicit multi-symplectic methods for Klein–Gordon–Schrödinger equations

(2009) Jialin Hong et al.   JOURNAL OF COMPUTATIONAL PHYSICS