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In this paper, we design a novel linearized and momentum-preserving Fourier pseudo-spectral scheme to solve the Rosenau-Korteweg de Vries equation. With the aid of a new semi-norm equivalence between the Fourier pseudo-spectral method and the finite difference method, a prior bound of the numerical solution in discrete $L^{infty}$-norm is obtained from the discrete momentum conservation law. Subsequently, based on the energy method and the bound of the numerical solution, we show that, without any restriction on the mesh ratio, the scheme is convergent with order $O(N^{-s}+tau^2)$ in discrete $L^infty$-norm, where $N$ is the number of collocation points used in the spectral method and $tau$ is the time step. Numerical results are addressed to confirm our theoretical analysis.
This paper proposes a new class of arbitarily high-order conservative numerical schemes for the generalized Korteweg-de Vries (KdV) equation. This approach is based on the scalar auxiliary variable (SAV) method. The equation is reformulated into an e
In this paper, we develop a new class of high-order energy-preserving schemes for the Korteweg-de Vries equation based on the quadratic auxiliary variable technique, which can conserve the original energy of the system. By introducing a quadratic aux
Original Whithams method of derivation of modulation equations is applied to systems whose dynamics is described by a perturbed Korteweg-de Vries equation. Two situations are distinguished: (i) the perturbation leads to appearance of right-hand sides
In this paper we consider two numerical scheme based on trapezoidal rule in time for the linearized KdV equation in one space dimension. The goal is to derive some suitable artificial boundary conditions for these two full discretization using Z-tran
The primary challenge in solving kinetic equations, such as the Vlasov equation, is the high-dimensional phase space. In this context, dynamical low-rank approximations have emerged as a promising way to reduce the high computational cost imposed by