Exponential collocation methods based on continuous finite element approximations for efficiently solving the cubic Schrödinger equation
From MaRDI portal
Publication:6088422
DOI10.1002/num.22501OpenAlexW3043395867WikidataQ114235278 ScholiaQ114235278MaRDI QIDQ6088422
Publication date: 14 December 2023
Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1002/num.22501
finite element methodscollocation methodscubic Schrödinger equationexponential integratorsenergy preservation
Related Items
Cites Work
- An energy-preserving and symmetric scheme for nonlinear Hamiltonian wave equations
- Adaptive splitting methods for nonlinear Schrödinger equations in the semiclassical regime
- Fractional error estimates of splitting schemes for the nonlinear Schrödinger equation
- Computational methods for the dynamics of the nonlinear Schrödinger/Gross-Pitaevskii equations
- Trigonometric collocation methods based on Lagrange basis polynomials for multi-frequency oscillatory second-order differential equations
- Effective approximation for the semiclassical Schrödinger equation
- The lack of continuity and the role of infinite and infinitesimal in numerical methods for ODEs: the case of symplecticity
- A simple framework for the derivation and analysis of effective one-step methods for ODEs
- Waves that appear from nowhere and disappear without a trace
- Geometric numerical integration and Schrödinger equations
- Energy conservation issues in the numerical solution of the semilinear wave equation
- The focusing nonlinear Schrödinger equation: Effect of the coupling to a low frequency field
- One-stage exponential integrators for nonlinear Schrödinger equations over long times
- Sharp well-posedness and ill-posedness results for a quadratic nonlinear Schrödinger equation
- Low-regularity bilinear estimates for a quadratic nonlinear Schrödinger equation
- Symmetric exponential integrators with an application to the cubic Schrödinger equation
- Conservation of energy, momentum and actions in numerical discretizations of non-linear wave equations
- From quantum to classical molecular dynamics: Reduced models and numerical analysis.
- Nonlinear Schrödinger equations and their spectral semi-discretizations over long times
- Splitting integrators for nonlinear Schrödinger equations over long times
- Conservation of phase space properties using exponential integrators on the cubic Schrödinger equation
- An energy-conserving Galerkin scheme for a class of nonlinear dispersive equations
- Exponential Runge-Kutta methods for the Schrödinger equation
- Symmetric and arbitrarily high-order Birkhoff-Hermite time integrators and their long-time behaviour for solving nonlinear Klein-Gordon equations
- Multi-symplectic Runge-Kutta collocation methods for Hamiltonian wave equations
- A class of energy-conserving Hamiltonian boundary value methods for nonlinear Schrödinger equation with wave operator
- Numerical methods and comparison for computing dark and bright solitons in the nonlinear Schrödinger equation
- Exponential time integration of solitary waves of cubic Schrödinger equation
- Long-time momentum and actions behaviour of energy-preserving methods for semi-linear wave equations via spatial spectral semi-discretisations
- Exponential collocation methods for conservative or dissipative systems
- Spectrally accurate space-time solution of Hamiltonian PDEs
- Efficient implementation of RKN-type Fourier collocation methods for second-order differential equations
- General local energy-preserving integrators for solving multi-symplectic Hamiltonian PDEs
- The boundness of the operator-valued functions for multidimensional nonlinear wave equations with applications
- Energy-conserving methods for the nonlinear Schrödinger equation
- Symplectic exponential Runge-Kutta methods for solving nonlinear Hamiltonian systems
- Preserving energy resp. dissipation in numerical PDEs using the ``Average Vector Field method
- Structure-Preserving Algorithms for Oscillatory Differential Equations II
- Exponential Integrators Preserving First Integrals or Lyapunov Functions for Conservative or Dissipative Systems
- Exponential integrators
- On splitting methods for Schrödinger-Poisson and cubic nonlinear Schrödinger equations
- Mathematical and computational methods for semiclassical Schrödinger equations
- A General Framework for Deriving Integral Preserving Numerical Methods for PDEs
- Partial Differential Equations and the Finite Element Method
- Splitting methods
- Energy Conserving Explicit Local Time Stepping for Second-Order Wave Equations
- Global Solutions for 3D Quadratic Schrodinger Equations
- Mollified Impulse Methods for Highly Oscillatory Differential Equations
- Order Estimates in Time of Splitting Methods for the Nonlinear Schrödinger Equation
- Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations
- Structure-Preserving Algorithms for Oscillatory Differential Equations
- Convergence Analysis of High-Order Time-Splitting Pseudospectral Methods for Nonlinear Schrödinger Equations
- A Continuous-Stage Modified Leap-Frog Scheme for High-Dimensional Semi-Linear Hamiltonian Wave Equations
- An Essential Extension of the Finite-Energy Condition for Extended Runge-Kutta-Nyström Integrators when Applied to Nonlinear Wave Equations
- Projected explicit lawson methods for the integration of Schrödinger equation
- The formulation and analysis of energy-preserving schemes for solving high-dimensional nonlinear Klein–Gordon equations
- Uniform and Optimal Error Estimates of an Exponential Wave Integrator Sine Pseudospectral Method for the Nonlinear Schrödinger Equation with Wave Operator
- Exponential Rosenbrock-Type Methods
- Numerical methods for Hamiltonian PDEs
- Geometric Numerical Integration
- Explicit Exponential Runge--Kutta Methods for Semilinear Parabolic Problems
- Functionally Fitted Energy-Preserving Methods for Solving Oscillatory Nonlinear Hamiltonian Systems
- Improved error estimates for splitting methods applied to highly-oscillatory nonlinear Schrödinger equations
- Multi-symplectic Fourier pseudospectral method for the nonlinear Schrödinger equation
- Geometric integrators for the nonlinear Schrödinger equation
- Arbitrary-order trigonometric Fourier collocation methods for multi-frequency oscillatory systems
- Compact schemes for laser-matter interaction in Schrödinger equation based on effective splittings of Magnus expansion
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
