Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
A comparison of Fourier pseudospectral methods for the solution of the Korteweg-de Vries equation
Journal of Computational Physics
Operator splitting methods for generalized Korteweg-de Vries equations
Journal of Computational Physics
A Local Discontinuous Galerkin Method for KdV Type Equations
SIAM Journal on Numerical Analysis
Multisymplectic box schemes and the Korteweg-de Vries equation
Applied Numerical Mathematics - Special issue: Workshop on innovative time integrators for PDEs
On Symplectic and Multisymplectic Schemes for the KdV Equation
Journal of Scientific Computing
Numerical Solution of Partial Differential Equations: An Introduction
Numerical Solution of Partial Differential Equations: An Introduction
Journal of Scientific Computing
Entropy-TVD Scheme for Nonlinear Scalar Conservation Laws
Journal of Scientific Computing
Journal of Computational Physics
Hi-index | 31.45 |
In this paper, we develop a finite-volume scheme for the KdV equation which conserves both the momentum and energy. The main ingredient of the method is a numerical device we developed in recent years that enables us to construct numerical method for a PDE that also simulates its related equations. In the method, numerical approximations to both the momentum and energy are conservatively computed. The operator splitting approach is adopted in constructing the method in which the conservation and dispersion parts of the equation are alternatively solved; our numerical device is applied in solving the conservation part of the equation. The feasibility and stability of the method is discussed, which involves an important property of the method, the so-called Jensen condition. The truncation error of the method is analyzed, which shows that the method is second-order accurate. Finally, several numerical examples, including the Zabusky-Kruskal's example, are presented to show the good stability property of the method for long-time numerical integration.