Linearly implicit and second-order energy-preserving schemes for the modified Korteweg-de Vries equation
DOI10.1007/s11075-022-01312-zzbMath1502.65166OpenAlexW4280585563MaRDI QIDQ2098794
Sihui Zheng, Ling Zhu, Jin-Liang Yan, Fu-Qiang Lu
Publication date: 22 November 2022
Published in: Numerical Algorithms (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11075-022-01312-z
Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) KdV equations (Korteweg-de Vries equations) (35Q53) 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) Extrapolation to the limit, deferred corrections (65B05) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)
Cites Work
- Unnamed Item
- Unnamed Item
- A direct discontinuous Galerkin method for the generalized Korteweg-de Vries equation: energy conservation and boundary effect
- A new high-order energy-preserving scheme for the modified Korteweg-de Vries equation
- Interaction properties of complex modified Korteweg-de Vries (mKdV) solitons
- A new approach for numerical solution of modified Korteweg-de Vries equation
- Solitary wave solutions of the MKdV\(^-\) equation
- The scalar auxiliary variable (SAV) approach for gradient flows
- A conservative Fourier pseudo-spectral method for the nonlinear Schrödinger equation
- Energy-stable Runge-Kutta schemes for gradient flow models using the energy quadratization approach
- A meshless method for solving mKdV equation
- A conservative compact finite difference scheme for the coupled Schrödinger-KdV equations
- A new efficient energy-preserving finite volume element scheme for the improved Boussinesq equation
- Highly efficient invariant-conserving explicit Runge-Kutta schemes for nonlinear Hamiltonian differential equations
- Arbitrarily high-order linear energy stable schemes for gradient flow models
- A new Lagrange multiplier approach for gradient flows
- Efficient modified techniques of invariant energy quadratization approach for gradient flows
- Locally conservative finite difference schemes for the modified KdV equation
- Efficient linear schemes with unconditional energy stability for the phase field elastic bending energy model
- A linearly implicit and local energy-preserving scheme for the sine-Gordon equation based on the invariant energy quadratization approach
- 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
- Conservative, discontinuous Galerkin–methods for the generalized Korteweg–de Vries equation
- Solutions to the modified Korteweg–de Vries equation
- Approximation Results for Orthogonal Polynomials in Sobolev Spaces
- The Korteweg–deVries Equation: A Survey of Results
- Korteweg-de Vries Equation and Generalizations. III. Derivation of the Korteweg-de Vries Equation and Burgers Equation
- Conservative, high-order numerical schemes for the generalized Korteweg—de Vries equation
- Optimal error estimates of finite difference methods for the Gross-Pitaevskii equation with angular momentum rotation
- The Exponential Scalar Auxiliary Variable (E-SAV) Approach for Phase Field Models and Its Explicit Computing
- Energy-Decaying Extrapolated RK--SAV Methods for the Allen--Cahn and Cahn--Hilliard Equations
- Arbitrarily High-Order Unconditionally Energy Stable Schemes for Thermodynamically Consistent Gradient Flow Models
- A New Class of Efficient and Robust Energy Stable Schemes for Gradient Flows
- Multi-symplectic Fourier pseudospectral method for the nonlinear Schrödinger equation
This page was built for publication: Linearly implicit and second-order energy-preserving schemes for the modified Korteweg-de Vries equation