Novel High-Order Mass- and Energy-Conservative Runge-Kutta Integrators for the Regularized Logarithmic Schrödinger Equation

DOI10.4208/nmtma.oa-2022-0185OpenAlexW4387337630MaRDI QIDQ6151343

Songhe Song, Xu Qian, Hong Zhang, JingYe Yan

Publication date: 11 March 2024

Published in: Numerical Mathematics: Theory, Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4208/nmtma.oa-2022-0185

zbMATH Keywords

diagonally implicit Runge-Kutta schemeinvariant energy quadratization approachregularized logarithmic Schrödinger equationconservative numerical integrators

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) NLS equations (nonlinear Schrödinger equations) (35Q55) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Cites Work

• Unnamed Item
• Unnamed Item
• Fourth-order compact and energy conservative difference schemes for the nonlinear Schrödinger equation in two dimensions
• A new error analysis of Crank-Nicolson Galerkin FEMs for a generalized nonlinear Schrödinger equation
• High-order compact splitting multisymplectic method for the coupled nonlinear Schrödinger equations
• Symplectic and multi-symplectic wavelet collocation methods for two-dimensional Schrödinger equations
• A linearly implicit conservative scheme for the coupled nonlinear Schrödinger equation
• Numerical approximations for the molecular beam epitaxial growth model based on the invariant energy quadratization method
• The scalar auxiliary variable (SAV) approach for gradient flows
• Local discontinuous Galerkin methods for nonlinear Schrödinger equations
• Symplectic and multi-symplectic methods for the nonlinear Schrödinger equation
• Two regularized energy-preserving finite difference methods for the logarithmic Klein-Gordon equation
• A novel regularized model for the logarithmic Klein-Gordon equation
• Highly efficient invariant-conserving explicit Runge-Kutta schemes for nonlinear Hamiltonian differential equations
• Novel high-order energy-preserving diagonally implicit Runge-Kutta schemes for nonlinear Hamiltonian ODEs
• Structure-preserving algorithms for the two-dimensional sine-Gordon equation with Neumann boundary conditions
• An efficient energy-preserving algorithm for the Lorentz force system
• Arbitrarily high-order energy-preserving schemes for the Camassa-Holm equation
• Linear and unconditionally energy stable schemes for the binary fluid-surfactant phase field model
• Regularized numerical methods for the logarithmic Schrödinger equation
• A linearly implicit and local energy-preserving scheme for the sine-Gordon equation based on the invariant energy quadratization approach
• Numerical solution of the regularized logarithmic Schrödinger equation on unbounded domains
• Local energy-preserving and momentum-preserving algorithms for coupled nonlinear Schrödinger system
• Preserving energy resp. dissipation in numerical PDEs using the ``Average Vector Field method
• Arbitrarily high-order unconditionally energy stable SAV schemes for gradient flow models
• A Simple Framework of Conservative Algorithms for the Coupled Nonlinear Schrödinger Equations with Multiply Components
• Spectral Methods
• Stability of Runge-Kutta Methods for Trajectory Problems
• A General Framework for Deriving Integral Preserving Numerical Methods for PDEs
• Methods for the Numerical Solution of the Nonlinear Schroedinger Equation
• Symplectic Geometric Algorithms for Hamiltonian Systems
• Numerical solution of isospectral flows
• Efficient Second Order Unconditionally Stable Schemes for a Phase Field Moving Contact Line Model Using an Invariant Energy Quadratization Approach
• Error Estimates of a Regularized Finite Difference Method for the Logarithmic Schrödinger Equation
• Convergence and Error Analysis for the Scalar Auxiliary Variable (SAV) Schemes to Gradient Flows
• Geometric properties of Kahan's method
• Error estimates of local energy regularization for the logarithmic Schrödinger equation
• Hamiltonian Boundary Value Method for the Nonlinear Schrödinger Equation and the Korteweg-de Vries Equation
• Arbitrarily High-Order Unconditionally Energy Stable Schemes for Thermodynamically Consistent Gradient Flow Models
• Improved uniform error bounds of the time-splitting methods for the long-time (nonlinear) Schrödinger equation
• Numerical Methods for Ordinary Differential Equations
• Symplectic methods for the nonlinear Schrödinger equation