Explicit high-order structure-preserving algorithms for the two-dimensional fractional nonlinear Schrödinger equation
DOI10.1080/00207160.2021.1940978zbMath1499.35638OpenAlexW3171268531MaRDI QIDQ5072017
Yayun Fu, Y. H. Shi, Yan-Min Zhao
Publication date: 25 April 2022
Published in: International Journal of Computer Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1080/00207160.2021.1940978
Runge-Kutta methodstructure-preserving algorithmsfractional nonlinear Schrödinger equationinvariant energy quadratizationexplicit conservative schemes
Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Fractional partial differential equations (35R11)
Cites Work
- Computational methods for the dynamics of the nonlinear Schrödinger/Gross-Pitaevskii equations
- A linearly implicit conservative difference scheme for the space fractional coupled nonlinear Schrödinger equations
- An energy conservative difference scheme for the nonlinear fractional Schrödinger equations
- Partitioned averaged vector field methods
- A parallel-in-time iterative algorithm for Volterra partial integro-differential problems with weakly singular kernel
- Hölder continuity of solutions of supercritical dissipative hydrodynamic transport equations
- Fractional quantum mechanics and Lévy path integrals
- Explicit methods based on a class of four stage fourth order Runge-Kutta methods for preserving quadratic laws
- Linear, first and second-order, unconditionally energy stable numerical schemes for the phase field model of homopolymer blends
- Numerical approximations for the molecular beam epitaxial growth model based on the invariant energy quadratization method
- A fast linearized conservative finite element method for the strongly coupled nonlinear fractional Schrödinger equations
- Error estimate of Fourier pseudo-spectral method for multidimensional nonlinear complex fractional Ginzburg-Landau equations
- Structure-preserving numerical methods for the fractional Schrödinger equation
- On the continuum limit for discrete NLS with long-range lattice interactions
- Maximum-norm error analysis of a conservative scheme for the damped nonlinear fractional Schrödinger equation
- Fourier pseudospectral method on generalized sparse grids for the space-fractional Schrödinger equation
- Mass-conservative Fourier spectral methods for solving the fractional nonlinear Schrödinger equation
- An explicit fourth-order energy-preserving scheme for Riesz space fractional nonlinear wave equations
- Fast dissipation-preserving difference scheme for nonlinear generalized wave equations with the integral fractional Laplacian
- Highly efficient invariant-conserving explicit Runge-Kutta schemes for nonlinear Hamiltonian differential equations
- An explicit structure-preserving algorithm for the nonlinear fractional Hamiltonian wave equation
- Efficient schemes for the damped nonlinear Schrödinger equation in high dimensions
- A conservative difference scheme for solving the strongly coupled nonlinear fractional Schrödinger equations
- An explicit dissipation-preserving method for Riesz space-fractional nonlinear wave equations in multiple dimensions
- A fourth-order dissipation-preserving algorithm with fast implementation for space fractional nonlinear damped wave equations
- Structure-preserving algorithms for the two-dimensional sine-Gordon equation with Neumann boundary conditions
- Two classes of linearly implicit local energy-preserving approach for general multi-symplectic Hamiltonian PDEs
- Symplectic scheme for the Schrödinger equation with fractional Laplacian
- A linearly implicit and local energy-preserving scheme for the sine-Gordon equation based on the invariant energy quadratization approach
- Existence of the global smooth solution to the period boundary value problem of fractional nonlinear Schrödinger equation
- Fractional Laplacian on the torus
- Global Well-Posedness for the Fractional Nonlinear Schrödinger Equation
- On the Preservation of Invariants by Explicit Runge--Kutta Methods
- Some physical applications of fractional Schrödinger equation
- Fully Discrete Second-Order Linear Schemes for Hydrodynamic Phase Field Models of Binary Viscous Fluid Flows with Variable Densities
- A Fourth-order Compact ADI scheme for Two-Dimensional Nonlinear Space Fractional Schrödinger Equation
- Numerical approximations for a phase field dendritic crystal growth model based on the invariant energy quadratization approach
- Geometric Numerical Integration
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