相关论文: Higher-order Continuum Approximation for Rarefied …

Langevin simulation provides an effective way to study collisional effects in beams by reducing the six-dimensional Fokker-Planck equation to a group of stochastic ordinary differential equations. These resulting equations usually have…

Solving inverse problems using Bayesian methods can become prohibitively expensive when likelihood evaluations involve complex and large scale numerical models. A common approach to circumvent this issue is to approximate the forward model…

The higher-order gas-kinetic scheme for solving the Navier-Stokes equations has been studied in recent years. In addition to the use of higher-order reconstruction techniques, many terms are used in the Taylor expansion of the gas…

This paper tackles the issue of establishing a lower-bound on the asymptotic ratio of survival probabilities between two different initial conditions, asymptotically in time for a given Markov process with extinction. Such a comparison is a…

We propose a communication- and computation-efficient distributed optimization algorithm using second-order information for solving ERM problems with a nonsmooth regularization term. Current second-order and quasi-Newton methods for this…

The so-called haptotaxis equation is a special class of transport equation that arises from models of biological cell movement along tissue fibers. This equation has an anisotropic advection-diffusion equation as its macroscopic limit. An…

We consider triangular arrays of Markov chains that converge weakly to a diffusion process. Second order Edgeworth type expansions for transition densities are proved. The paper differs from recent results in two respects. We allow…

We present a new and relatively elementary method for studying the solution of the initial-value problem for dispersive linear and integrable equations in the large-$t$ limit, based on a generalization of steepest descent techniques for…

Self-diffusion along the longitudinal coordinate in a channel of varying cross section is considered. The starting point is the two-dimensional Enskog-Boltzmann-Lorentz kinetic equation with appropriated boundary conditions. It is…

Asymptotic normality of extreme value tail estimators received much attention in the literature, giving rise to increasingly complicated 2nd order regularity conditions. However, such conditions are really difficult to be checked for real…

In this paper, we study a time discrete scheme for the initial value problem of the ES-BGK kinetic equation. Numerically solving these equations are challenging due to the nonlinear stiff collision (source) terms induced by small mean free…

In this paper an even higher-order compact GKS up to sixth order of accuracy will be constructed for the shock and acoustic wave computation on unstructured mesh. The compactness is defined by the physical domain of dependence for an…

We propose a numerical approach, of the BGK kinetic type, that is able to approximate with a given, but arbitrary, order of accuracy the solution of linear and non-linear convection-diffusion type problems: scalar advection-diffusion,…

Motivated by the problem of solving the Einstein equations, we discuss high order finite difference discretizations of first order in time, second order in space hyperbolic systems.Particular attention is paid to the case when first order…

We introduce a numerical method for solving Grad's moment equations or regularized moment equations for arbitrary order of moments. In our algorithm, we do not need explicitly the moment equations. As an instead, we directly start from the…

This paper presents an investigation into the high-order asymptotic expansion for 2D and 3D cubic nonlinear Klein-Gordon equations in the non-relativistic limit regime. There are extensive numerical and analytic results concerning that the…

In this study, we investigate the Shallow Water Equations incorporating source terms accounting for Manning friction and a non-flat bottom topology. Our primary focus is on developing and validating numerical schemes that serve a dual…

In this report we obtain higher order asymptotic expansions of solutions to wave equations with frictional and viscoelastic damping terms. Although the diffusion phenomena are dominant, differences between the solutions we deal with and…

Nonlinear/non-Gaussian filtering has broad applications in many areas of life sciences where either the dynamic is nonlinear and/or the probability density function of uncertain state is non-Gaussian. In such problems, the accuracy of the…

This paper introduces weighted finite difference methods for numerically solving dispersive evolution equations with solutions that are highly oscillatory in both space and time. We consider a semiclassically scaled cubic nonlinear…