Time second‐order splitting conservative difference scheme for nonlinear fractional Schrödinger equation

DOI10.1002/mma.8790OpenAlexW4306691341MaRDI QIDQ6182061

Jianqiang Xie, Muhammad Aamir Ali, Zhi-Yue Zhang

Publication date: 20 December 2023

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.8790

zbMATH Keywords

convergencesplittingfinite difference methodsunconditionally stablenonlinear fractional Schrödinger equation

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Fractional partial differential equations (35R11)

Cites Work

• Point-wise error estimate of a conservative difference scheme for the fractional Schrödinger equation
• Fast alternating-direction finite difference methods for three-dimensional space-fractional diffusion equations
• A fourth-order approximation of fractional derivatives with its applications
• Analysis of the linearly energy- and mass-preserving finite difference methods for the coupled Schrödinger-Boussinesq equations
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• On the conservation of fractional nonlinear Schrödinger equation's invariants by the local discontinuous Galerkin method
• Finite element method for nonlinear Riesz space fractional diffusion equations on irregular domains
• A fast linearized conservative finite element method for the strongly coupled nonlinear fractional Schrödinger equations
• Mass- and energy-conserving difference schemes for nonlinear fractional Schrödinger equations
• Split-step alternating direction implicit difference scheme for the fractional Schrödinger equation in two dimensions
• Mass-conservative Fourier spectral methods for solving the fractional nonlinear Schrödinger equation
• An analysis of implicit conservative difference solver for fractional Klein-Gordon-Zakharov system
• Linear implicit finite difference methods with energy conservation property for space fractional Klein-Gordon-Zakharov system
• Numerical soliton solutions of fractional Newell-Whitehead-Segel equation in binary fluid mixtures
• A structure preserving difference scheme with fast algorithms for high dimensional nonlinear space-fractional Schrödinger equations
• Structure-preserving algorithms for the two-dimensional fractional Klein-Gordon-Schrödinger equation
• A conservative difference scheme for solving the strongly coupled nonlinear fractional Schrödinger equations
• A Crank-Nicolson ADI quadratic spline collocation method for two-dimensional Riemann-Liouville space-fractional diffusion equations
• Existence of the global smooth solution to the period boundary value problem of fractional nonlinear Schrödinger equation
• Energy-conserved splitting FDTD methods for Maxwell's equations
• Numerical studies on the split-step finite difference method for nonlinear Schrödinger equations
• Energy-Conserved Splitting Finite-Difference Time-Domain Methods for Maxwell's Equations in Three Dimensions
• Split-Step Methods for the Solution of the Nonlinear Schrödinger Equation
• Numerical Study of Time-Splitting Spectral Discretizations of Nonlinear Schrödinger Equations in the Semiclassical Regimes
• Boundary Problems for the Fractional and Tempered Fractional Operators
• A novel method for new solutions of time fractional (1+2)-dimensional nonlinear Schrödinger equation involving dual-power law nonlinearity
• A Crank--Nicolson ADI Spectral Method for a Two-Dimensional Riesz Space Fractional Nonlinear Reaction-Diffusion Equation
• A Fourth-Order Time-Splitting Laguerre--Hermite Pseudospectral Method for Bose--Einstein Condensates
• A linearly implicit conservative scheme for the fractional nonlinear Schrödinger equation with wave operator

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