A linearly-implicit structure-preserving exponential time differencing scheme for Hamiltonian PDEs

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Cites Work

Unnamed Item
Partitioned averaged vector field methods
Symmetric exponential integrators with an application to the cubic Schrödinger equation
Partial differential equations. III: Nonlinear equations.
Conservation of phase space properties using exponential integrators on the cubic Schrödinger equation
A new class of time discretization schemes for the solution of nonlinear PDEs
Linear, first and second-order, unconditionally energy stable numerical schemes for the phase field model of homopolymer blends
The scalar auxiliary variable (SAV) approach for gradient flows
A conservative Fourier pseudo-spectral method for the nonlinear Schrödinger equation
Optimal error estimate of a linear Fourier pseudo-spectral scheme for two dimensional Klein-Gordon-Schrödinger equations
Runge-Kutta-Nyström methods adapted to the numerical integration of perturbed oscillators
Finite difference schemes for \(\frac{\partial u}{\partial t}=(\frac{\partial}{\partial x})^\alpha\frac{\delta G}{\delta u}\) that inherit energy conservation or dissipation property
Maximum-norm error analysis of a conservative scheme for the damped nonlinear fractional Schrödinger equation
A linearly implicit energy-preserving exponential integrator for the nonlinear Klein-Gordon equation
Efficient schemes for the damped nonlinear Schrödinger equation in high dimensions
Structure-preserving algorithms for the two-dimensional fractional Klein-Gordon-Schrödinger equation
A class of energy-conserving Hamiltonian boundary value methods for nonlinear Schrödinger equation with wave operator
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
Convergence analysis for the invariant energy quadratization (IEQ) schemes for solving the Cahn-Hilliard and Allen-Cahn equations with general nonlinear potential
A linearly implicit and local energy-preserving scheme for the sine-Gordon equation based on the invariant energy quadratization approach
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
Fast high-order compact exponential time differencing Runge-Kutta methods for second-order semilinear parabolic equations
Exponential Integrators Preserving First Integrals or Lyapunov Functions for Conservative or Dissipative Systems
Exponential integrators
Hamiltonian Boundary Value Methods (Energy Conserving Discrete Line Integral Methods)
Discrete Variational Derivative Method
A General Framework for Deriving Integral Preserving Numerical Methods for PDEs
Simulating Hamiltonian Dynamics
Symplectic Geometric Algorithms for Hamiltonian Systems
Fully Discrete Second-Order Linear Schemes for Hydrodynamic Phase Field Models of Binary Viscous Fluid Flows with Variable Densities
Maximum Principle Preserving Exponential Time Differencing Schemes for the Nonlocal Allen--Cahn Equation
Convergence and Error Analysis for the Scalar Auxiliary Variable (SAV) Schemes to Gradient Flows
The Exponential Scalar Auxiliary Variable (E-SAV) Approach for Phase Field Models and Its Explicit Computing
A Fourth-order Compact ADI scheme for Two-Dimensional Nonlinear Space Fractional Schrödinger Equation
A New Class of Efficient and Robust Energy Stable Schemes for Gradient Flows
A Sixth Order Averaged Vector Field Method
Multi-Symplectic Fourier Pseudospectral Method for the Kawahara Equation
Functions of Matrices
Geometric Numerical Integration
Multi-symplectic Fourier pseudospectral method for the nonlinear Schrödinger equation
Dissipative or conservative finite-difference schemes for complex-valued nonlinear partial differential equations
A linearly-implicit and conservative Fourier pseudo-spectral method for the 3D Gross-Pitaevskii equation with angular momentum rotation

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