Linearly-fitted energy-mass-preserving schemes for Korteweg-de Vries equations

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Numerical investigation of stability of solutions to ordinary differential equations (65L07)

Cites Work

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A direct discontinuous Galerkin method for the generalized Korteweg-de Vries equation: energy conservation and boundary effect
Some new structure-preserving algorithms for general multi-symplectic formulations of Hamiltonian PDEs
Operator splitting methods for generalized Korteweg-de Vries equations
Method of lines solution of the Korteweg-de Vries equation
Accuracy and conservation properties in numerical integration: The case of the Korteweg-de Vries equation
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.
A particle method for the KdV equation
Energy-conserving Hamiltonian boundary value methods for the numerical solution of the Korteweg-de Vries equation
Applications of KdV
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
Energy-preserving exponential integrators of arbitrarily high order for conservative or dissipative systems with highly oscillatory solutions
Efficient energy-preserving exponential integrators for multi-component Hamiltonian systems
A numerical method to compute the scattering solution for the KdV equation
Spectrally accurate space-time solution of Hamiltonian PDEs
Energy preserving integration of bi-Hamiltonian partial differential equations
Preserving energy resp. dissipation in numerical PDEs using the ``Average Vector Field method
High-order compact schemes for nonlinear dispersive waves
Korteweg-de Vries equation: a completely integrable Hamiltonian system
Time integration and discrete Hamiltonian systems
On spectral approximations using modified Legendre rational functions: Application to the Korteweg-de Vries equation on the half line
Exponential Integrators Preserving First Integrals or Lyapunov Functions for Conservative or Dissipative Systems
Conservative, discontinuous Galerkin–methods for the generalized Korteweg–de Vries equation
Exponential integrators
Numerical algorithms for solutions of Korteweg-de Vries equation
Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
Splitting methods
A Conservative Finite Element Method for the Korteweg-de Vries Equation
A New Dual-Petrov-Galerkin Method for Third and Higher Odd-Order Differential Equations: Application to the KDV Equation
Method for Solving the Korteweg-deVries Equation
Multisymplectic geometry and multisymplectic Preissmann scheme for the KdV equation
Korteweg-de Vries Equation and Generalizations. I. A Remarkable Explicit Nonlinear Transformation
Korteweg-de Vries Equation and Generalizations. II. Existence of Conservation Laws and Constants of Motion
An extended discrete gradient formula for oscillatory Hamiltonian systems
Energy-Preserving Continuous-Stage Exponential Runge--Kutta Integrators for Efficiently Solving Hamiltonian Systems
An Embedded Exponential-Type Low-Regularity Integrator for mKdV Equation
Multisymplectic box schemes for the complex modified Korteweg–de Vries equation
Functions of Matrices
Geometric Numerical Integration

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