相关论文: Convergence of a numerical scheme for a coupled Sc…

We consider the numerical approximation of a system of partial differential equations involving a nonlinear Schr\"odinger equation coupled with a hyperbolic conservation law. This system arises in models for the interaction of short and…

The KdV equation models the propagation of long waves in dispersive media, while the NLS equation models the dynamics of narrow-bandwidth wave packets consisting of short dispersive waves. A system that couples the two equations to model…

We prove strong convergence of a semi-discrete finite difference method for the KdV and modified KdV equations. We extend existing results to non-smooth data (namely, in $L^2$), without size restrictions. Our approach uses a fourth order…

In this work we present the convergence of a positivity preserving semi-discrete finite volume scheme for a coupled system of two non-local partial differential equations with cross-diffusion. The key to proving the convergence result is to…

We are concerned with the convergence of a numerical scheme for the initial-boundary value problem associated to the Korteweg-de Vries- Kawahara equation (in short Kawahara equation), which is a transport equation perturbed by dispersive…

We analyze a semi-implicit finite volume scheme for the Gray--Scott system, a model for pattern formation in chemical and biological media. We prove unconditional well-posedness of the fully discrete problem and establish qualitative…

We prove convergence of a fully discrete finite difference scheme for the Korteweg--de Vries equation. Both the decaying case on the full line and the periodic case are considered. If the initial data $u|_{t=0}=u_0$ is of high regularity,…

We design a consistent Galerkin scheme for the approximation of the vectorial modified Korteweg-de Vries equation. We demonstrate that the scheme conserves energy up to machine precision. In this sense the method is consistent with the…

The norm resolvent convergence of discrete Schr\"odinger operators to a continuum Schr\"odinger operator in the continuum limit is proved under relatively weak assumptions. This result implies, in particular, the convergence of the spectrum…

A conforming finite element scheme with mixed explicit-implicit time discretization for quasi-incompressible Navier-Stokes-Maxwell-Stefan systems in a bounded domain with periodic boundary conditions is presented. The system consists of the…

It is universally accepted that the cubic, nonlinear Schrodinger equation (NLS) models the dynamics of narrow-bandwidth wave packets consisting of short dispersive waves, while the Kortewegde Vries equation (KdV) models the propagation of…

This article is devoted to the analysis of the convergence rates of several nu- merical approximation schemes for linear and nonlinear Schr\"odinger equations on the real line. Recently, the authors have introduced viscous and two-grid…

We prove convergence of a finite difference approximation of the compressible Navier--Stokes system towards the strong solution in $R^d,$ $d=2,3,$ for the adiabatic coefficient $\gamma>1$. Employing the relative energy functional, we find a…

We prove existence and stability results for a two-parameter family of solitary-wave solutions to a system in which an equation of nonlinear Schr\"odinger type is coupled to an equation of Korteweg-de Vries type. Such systems model…

We consider families of solitary waves in the Korteweg--de Vries (KdV) equation coupled with the linear Schr\"{o}dinger (LS) equation. This model has been used to describe interactions between long and short waves. To characterize families…

In this paper, we propose a family of time-stepping schemes for approximating general nonlinear Schr\"odinger equations. The proposed schemes all satisfy both mass conservation and energy conservation. Truncation and dispersion error…

Numerical schemes that conserve invariants have demonstrated superior performance in various contexts, and several unified methods have been developed for constructing such schemes. However, the mathematical properties of these schemes…

We propose a finite volume scheme for convection-diffusion equations with nonlinear diffusion. Such equations arise in numerous physical contexts. We will particularly focus on the drift-diffusion system for semiconductors and the porous…

We are concerned with the convergence of a numerical scheme for the initial value problem associated to the $2 \times 2$ Keyfitz-Kranzer system of equations. In this paper we prove the convergence of a finite difference scheme to a weak…

In this paper a nonlinear coupled Schrodinger system in the presence of mixed cubic and superlinear power laws is considered. A non standard numerical method is developed to approximate the solutions in higher dimensional case. The idea…