Remarks on -additive spaces
The Runge-Kutta local projection -discontinuous-Galerkin finite element method for scalar conservation laws
Local smooth solution and non-relativistic limit of radiation hydrodynamics equations.
Central local discontinuous galerkin methods on overlapping cells for diffusion equations
In this paper we present two versions of the central local discontinuous Galerkin (LDG) method on overlapping cells for solving diffusion equations, and provide their stability analysis and error estimates for the linear heat equation. A comparison between the traditional LDG method on a single mesh and the two versions of the central LDG method on overlapping cells is also made. Numerical experiments are provided to validate the quantitative conclusions from the analysis and to support conclusions...
Global asymptotic stability of 3-species mutualism models with diffusion and delay effects.
The numerical convergence of the Landau-Lifshitz equations and its simulation.
Asymptotic behavior of equilibrium point for a family of rational difference equations.
Positive solution of singular boundary value problem for a nonlinear fractional differential equation.
Central local discontinuous galerkin methods on overlapping cells for diffusion equations
In this paper we present two versions of the central local discontinuous Galerkin (LDG) method on overlapping cells for solving diffusion equations, and provide their stability analysis and error estimates for the linear heat equation. A comparison between the traditional LDG method on a single mesh and the two versions of the central LDG method on overlapping cells is also made. Numerical experiments are provided to validate the quantitative conclusions from the analysis and to support conclusions...
stability analysis of the central discontinuous Galerkin method and a comparison between the central and regular discontinuous Galerkin methods
We prove stability and derive error estimates for the recently introduced central discontinuous Galerkin method, in the context of linear hyperbolic equations with possibly discontinuous solutions. A comparison between the central discontinuous Galerkin method and the regular discontinuous Galerkin method in this context is also made. Numerical experiments are provided to validate the quantitative conclusions from the analysis.
Discontinuous Galerkin method with Godunov-like numerical fluxes for traffic flows on networks. Part II: Maximum principle
We prove the maximum principle for a discontinuous Galerkin (DG) method applied to the numerical solution of traffic flow problems on networks described by the Lighthill-Whitham-Richards equations. The paper is a followup of the preceding paper, Part I, where stability of the scheme is analyzed. At traffic junctions, we consider numerical fluxes based on Godunov’s flux derived in our previous work. We also construct a new Godunov-like numerical flux taking into account right of way at the junction...
Discontinuous Galerkin method with Godunov-like numerical fluxes for traffic flows on networks. Part I: stability
We study the stability of a discontinuous Galerkin (DG) method applied to the numerical solution of traffic flow problems on networks. We discretize the Lighthill-Whitham-Richards equations on each road by DG. At traffic junctions, we consider two types of numerical fluxes that are based on Godunov’s numerical flux derived in a previous work of ours. These fluxes are easily constructible for any number of incoming and outgoing roads, respecting the drivers’ preferences. The analysis is split into...
Asymptotic stability for a class of nonlinear difference equations.
On Integrable Representations.
Existence and non-existence of global solutions for nonlinear hyperbolic equations of higher order
The existence and uniqueness of classical global solution and blow up of non-global solution to the first boundary value problem and the second boundary value problem for the equation are proved. Finally, the results of the above problem are applied to the equation arising from nonlinear waves in elastic rods
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