Artificial boundary conditions for the semi-discretized one-dimensional nonlocal Schrödinger equation

Derivation and analysis of computational methods for fractional Laplacian equations with absorbing layers

(2020) X. Antoine et al.   NUMERICAL ALGORITHMS

Towards Perfectly Matched Layers for time-dependent space fractional PDEs

(2019) Xavier Antoine et al.   JOURNAL OF COMPUTATIONAL PHYSICS

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

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

Accurate artificial boundary conditions for the semi-discretized linear Schrödinger and heat equations on rectangular domains

(2018) Songsong Ji et al.   COMPUTER PHYSICS COMMUNICATIONS

Boundary conditions for fractional diffusion

(2018) Boris Baeumer et al.   JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

Numerical Solution of a Two-Dimensional Nonlocal Wave Equation on Unbounded Domains

(2018) Qiang Du et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Boundary conditions for two-sided fractional diffusion

(2018) James F. Kelly et al.   JOURNAL OF COMPUTATIONAL PHYSICS

A friendly review of absorbing boundary conditions and perfectly matched layers for classical and relativistic quantum waves equations

(2017) X. Antoine et al.   MOLECULAR PHYSICS

The locally extrapolated exponential splitting scheme for multi-dimensional nonlinear space-fractional Schrödinger equations

(2017) X. Liang et al.   NUMERICAL ALGORITHMS

Numerical Solution of the Nonlocal Diffusion Equation on the Real Line

(2017) Chunxiong Zheng et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Artificial Boundary Conditions for Nonlocal Heat Equations on Unbounded Domain

(2016) Wei Zhang et al.   Communications in Computational Physics

On the ground states and dynamics of space fractional nonlinear Schrödinger/Gross–Pitaevskii equations with rotation term and nonlocal nonlinear interactions

(2016) Xavier Antoine et al.   JOURNAL OF COMPUTATIONAL PHYSICS

A fourth-order implicit-explicit scheme for the space fractional nonlinear Schrödinger equations

(2016) A. Q. M. Khaliq et al.   NUMERICAL ALGORITHMS

Fractional Schrödinger dynamics and decoherence

(2016) Kay Kirkpatrick et al.   PHYSICA D-NONLINEAR PHENOMENA

A fully spectral collocation approximation for multi-dimensional fractional Schrödinger equations

(2015) A.H. Bhrawy et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Fractional quantum mechanics in polariton condensates with velocity-dependent mass

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

Efficient sum-of-exponentials approximations for the heat kernel and their applications

(2014) Shidong Jiang et al.   ADVANCES IN COMPUTATIONAL MATHEMATICS

Asymptotically Compatible Schemes and Applications to Robust Discretization of Nonlocal Models

(2014) Xiaochuan Tian et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Computational methods for the dynamics of the nonlinear Schrödinger/Gross–Pitaevskii equations

(2013) Xavier Antoine et al.   COMPUTER PHYSICS COMMUNICATIONS

Ground state solutions for nonlinear fractional Schrödinger equations in RN

(2013) Simone Secchi   JOURNAL OF MATHEMATICAL PHYSICS

Analysis and Comparison of Different Approximations to Nonlocal Diffusion and Linear Peridynamic Equations

(2013) Xiaochuan Tian et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

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

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

Matching boundary conditions for lattice dynamics

(2012) X. Wang et al.   INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING