A structure-preserving local discontinuous Galerkin method for the stochastic KdV equation
DOI10.1016/j.apnum.2024.06.001zbMATH Open1546.65072MaRDI QIDQ6593393
Xiao-Hua Ding, Qiang Ma, Zhanwen Yang, Xue-wei Liu
Publication date: 26 August 2024
Published in: Applied Numerical Mathematics (Search for Journal in Brave)
KdV equations (Korteweg-de Vries equations) (35Q53) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) PDEs with randomness, stochastic partial differential equations (35R60) Numerical methods for Hamiltonian systems including symplectic integrators (65P10)
Cites Work
- Unnamed Item
- Unnamed Item
- Multi-symplectic methods for the Itô-type coupled KdV equation
- Multi-symplectic splitting method for the coupled nonlinear Schrödinger equation
- A compact difference scheme for the fractional diffusion-wave equation
- A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations
- Some new structure-preserving algorithms for general multi-symplectic formulations of Hamiltonian PDEs
- Preservation of physical properties of stochastic Maxwell equations with additive noise via stochastic multi-symplectic methods
- Splitting multisymplectic integrators for Maxwell's equations
- Backward error analysis for multi-symplectic integration methods
- Multisymplectic box schemes and the Korteweg-de Vries equation.
- On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves.
- Local discontinuous Galerkin methods for partial differential equations with higher order derivatives
- An energy-conserving method for stochastic Maxwell equations with multiplicative noise
- Structure-preserving numerical methods for the fractional Schrödinger equation
- Local discontinuous Galerkin methods for nonlinear Schrödinger equations
- Optimal convergence and long-time conservation of exponential integration for Schrödinger equations in a normal or highly oscillatory regime
- Multi-symplectic discontinuous Galerkin methods for the stochastic Maxwell equations with additive noise
- Stochastic discontinuous Galerkin methods (SDGM) based on fluctuation-dissipation balance
- Symplectic wavelet collocation method for Hamiltonian wave equations
- Galerkin finite element method for the nonlinear fractional Ginzburg-Landau equation
- \(L^\infty\) error estimates of discontinuous Galerkin methods for delay differential equations
- Energy-conserved splitting FDTD methods for Maxwell's equations
- Numerical studies of the stochastic Korteweg-de Vries equation
- Numerical solution of Korteweg-de Vries equation by Galerkin B-spline finite element method
- Hamiltonian Boundary Value Methods (Energy Conserving Discrete Line Integral Methods)
- Simulating Hamiltonian Dynamics
- On the excitation of long nonlinear water waves by a moving pressure distribution
- Generation of upstream advancing solitons by moving disturbances
- The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
- A Local Discontinuous Galerkin Method for KdV Type Equations
- A Trigonometric Method for the Linear Stochastic Wave Equation
- A local discontinuous Galerkin method for nonlinear parabolic SPDEs
- Linearly Implicit Local and Global Energy-Preserving Methods for PDEs with a Cubic Hamiltonian
- Error estimates of finite element method for semilinear stochastic strongly damped wave equation
- Nonlinearization of spectral problems for the perturbation KdV systems
- Numerical conservation issues for the stochastic Korteweg-de Vries equation
- Local structure-preserving algorithms for general multi-symplectic Hamiltonian PDEs
This page was built for publication: A structure-preserving local discontinuous Galerkin method for the stochastic KdV equation