Optimal error bounds of the time-splitting sine-pseudospectral method for the biharmonic nonlinear Schrödinger equation
DOI10.1016/j.apnum.2024.09.007MaRDI QIDQ6646524
Publication date: 2 December 2024
Published in: Applied Numerical Mathematics (Search for Journal in Brave)
energy methoderror boundStrang splittingtime-splitting pseudospectral methodbiharmonic nonlinear Schrödinger equation
NLS equations (nonlinear Schrödinger equations) (35Q55) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Time-dependent Schrödinger equations and Dirac equations (35Q41)
Cites Work
- Unnamed Item
- Computational methods for the dynamics of the nonlinear Schrödinger/Gross-Pitaevskii equations
- Optimal \(l^\infty\) error estimates of finite difference methods for the coupled Gross-Pitaevskii equations in high dimensions
- Well-posedness of higher-order nonlinear Schrödinger equations in Sobolev spaces \(H^{s}(\mathbb R^{n})\) and applications
- Global well-posedness for energy critical fourth-order Schrödinger equations in the radial case
- The cubic fourth-order Schrödinger equation
- Short proof of a discrete Gronwall inequality
- The nonlinear Schrödinger equation. Self-focusing and wave collapse
- Stability of solitons described by nonlinear Schrödinger-type equations with higher-order dispersion
- Quasi-invariant Gaussian measures for the cubic fourth order nonlinear Schrödinger equation
- Periodic fourth-order cubic NLS: local well-posedness and non-squeezing property
- Numerical solution of the Gross--Pitaevskii equation for Bose--Einstein condensation
- Mathematical theory and numerical methods for Bose-Einstein condensation
- Error analysis of the Strang time-splitting Laguerre-Hermite/Hermite collocation methods for the Gross-Pitaevskii equation
- Stabilization and control for the biharmonic Schrödinger equation
- The initial-boundary value problem for the biharmonic Schrödinger equation on the half-line
- Lower regularity solutions of the biharmonic Schrödinger equation in a quarter plane
- Operator-compensation methods with mass and energy conservation for solving the Gross-Pitaevskii equation
- An efficient and spectrally accurate numerical method for computing dynamics of rotating Bose-Einstein condensates
- Spectral Methods
- Singular solutions of theL2-supercritical biharmonic nonlinear Schrödinger equation
- On splitting methods for Schrödinger-Poisson and cubic nonlinear Schrödinger equations
- Solving Ordinary Differential Equations I
- Self-Focusing with Fourth-Order Dispersion
- A Generalized-Laguerre–Fourier–Hermite Pseudospectral Method for Computing the Dynamics of Rotating Bose–Einstein Condensates
- The Fourth-Order Dispersive Nonlinear Schrödinger Equation: Orbital Stability of a Standing Wave
- Splitting methods
- Split-Step Methods for the Solution of the Nonlinear Schrödinger Equation
- Orbitally Stable Standing Waves of a Mixed Dispersion Nonlinear Schrödinger Equation
- Dispersion estimates for fourth order Schrödinger equations
- Error estimates at low regularity of splitting schemes for NLS
- Uniform and Optimal Error Estimates of an Exponential Wave Integrator Sine Pseudospectral Method for the Nonlinear Schrödinger Equation with Wave Operator
- Singular Solutions of the Biharmonic Nonlinear Schrödinger Equation
- Geometric Numerical Integration
- Dynamics of Rotating Bose--Einstein Condensates and its Efficient and Accurate Numerical Computation
- Well-Posedness and Exact Controllability of Fourth Order Schrödinger Equation with Boundary Control and Collocated Observation
- A Fourth-Order Time-Splitting Laguerre--Hermite Pseudospectral Method for Bose--Einstein Condensates
- Improved uniform error bounds of the time-splitting methods for the long-time (nonlinear) Schrödinger equation
- Error estimates of the time-splitting methods for the nonlinear Schrödinger equation with semi-smooth nonlinearity
- Error estimates of finite difference methods for the biharmonic nonlinear Schrödinger equation
- Optimal error bounds on time-splitting methods for the nonlinear Schrödinger equation with low regularity potential and nonlinearity
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