Pseudospectra of Linear Operators
SIAM Review
Journal of Computational Physics
Multi-symplectic Runge-Kutta collocation methods for Hamiltonian wave equations
Journal of Computational Physics
Multisymplectic box schemes and the Korteweg-de Vries equation
Applied Numerical Mathematics - Special issue: Workshop on innovative time integrators for PDEs
Journal of Computational Physics
Numerical method satisfying the first two conservation laws for the Korteweg-de Vries equation
Journal of Computational Physics
Time behaviour of the error when simulating finite-band periodic waves. The case of the KdV equation
Journal of Computational Physics
Dispersive properties of multisymplectic integrators
Journal of Computational Physics
An energy-conserving Galerkin scheme for a class of nonlinear dispersive equations
Journal of Computational Physics
Dispersion, group velocity, and multisymplectic discretizations
Mathematics and Computers in Simulation
Conservative numerical schemes for the Ostrovsky equation
Journal of Computational and Applied Mathematics
Applied Numerical Mathematics
Geometric numerical schemes for the KdV equation
Computational Mathematics and Mathematical Physics
Hi-index | 0.03 |
We examine some symplectic and multisymplectic methods for the notorious Korteweg---de Vries equation, with the question whether the added structure preservation that these methods offer is key in providing high quality schemes for the long time integration of nonlinear, conservative partial differential equations. Concentrating on second order discretizations, several interesting schemes are constructed and studied. Our essential conclusions are that it is possible to design very stable, conservative difference schemes for the nonlinear, conservative KdV equation. Among the best of such schemes are methods which are symplectic or multisymplectic. Semi-explicit, symplectic schemes can be very effective in many situations. Compact box schemes are effective in ensuring that no artificial wiggles appear in the approximate solution. A family of box schemes is constructed, of which the multisymplectic box scheme is a prominent member, which are particularly stable on coarse space---time grids