相关论文: Simple remedy for spurious states in discrete k(do…

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…

The goal of this work is to determine classes of travelling solitary wave solutions for a differential approximation of a finite difference scheme by means of a hyperbolic ansatz. It is shown that spurious solitary waves can occur in…

This paper proposes specular differentiation in one-dimensional Euclidean space and provides its fundamental analysis, including a quasi-Fermat theorem and a quasi-Mean Value Theorem. As an application, this paper develops several numerical…

Spurious currents, which are often observed near a curved interface in the multiphase simulations by diffuse interface methods, are unphysical phenomena and usually damage the computational accuracy and stability. In this paper, the…

To solve the Dirac equation with the finite difference method, one has to face up to the spurious-state problem due to the fermion doubling problem when using the conventional central difference formula to calculate the first-order…

Surface probes such as scanning tunneling microscopy (STM) have detected complex patterns at the nanoscale, indicative of electronic inhomogeneity, in a variety of high temperature superconductors. In cuprates, the pattern formation is…

We calculate scattering interference patterns for various electronic states proposed for the pseudogap regime of the cuprate superconductors. The scattering interference models all produce patterns whose wavelength changes as a function of…

Discretizing the Dirac equation on a uniform grid with the central difference formula often generates spurious states. We propose a staggered-grid scheme in the framework of the finite-difference method that suppresses these spurious states…

Scale-separated AdS compactifications of string theory can be constructed at the two-derivative supergravity level in the presence of smeared orientifold planes. The unsmearing corrections are known to leading order in the large volume,…

We compare some first order well-balanced numerical schemes for shallow water system with special interest in applications where there are abrupt variations of the topography. We show that the space step required to obtain a prescribed…

We reconsider the effect of disorder on the properties of a superconductor characterized by a sign-changing order parameter appropriate for Fe-based materials. Within a simple two band model, we calculate simultaneously $T_c$, the change in…

This paper aims to develop and analyze a numerical scheme for solving the backward problem of semilinear subdiffusion equations. We establish the existence, uniqueness, and conditional stability of the solution to the inverse problem by…

In this paper, we introduce a novel category of central compact schemes inspired by existing cell-node and cell-centered compact finite difference schemes, that offer a superior spectral resolution for solving the dispersive wave equation.…

We introduce a novel class of finite difference approximations, termed zigzag schemes, that employ a hybrid stencil that is neither symmetrical, nor fully one-sided. These zigzag schemes often enjoy more permissive stability constraints and…

In this paper a multi-band envelope-function Hamiltonian for lattice-matched semiconductor heterostructures is derived from first-principles norm-conserving pseudopotentials. The theory is applicable to isovalent or heterovalent…

In this work we explore the fidelity of numerical approximations to the analytic spectra of hyperbolic partial differential equation systems with variable coefficients. We are particularly interested in the ability of discrete methods to…

We derive high-order compact finite difference schemes for option pricing in stochastic volatility models on non-uniform grids. The schemes are fourth-order accurate in space and second-order accurate in time for vanishing correlation. In…

In this paper, we consider a sorting scheme for potentially spurious scattering resonant pairs in one- and two-dimensional electromagnetic problems and in three-dimensional acoustic problems. The novel sorting scheme is based on a…

In this paper, two kinds of high-order compact finite difference schemes for second-order derivative are developed. Then a second-order numerical scheme for Riemann-Liouvile derivative is established based on fractional center difference…

We use the linear scalar SDE as a test problem to show that it is possible to construct almost sure stable first-order weak balanced schemes based on the addition of stabilizing functions to the drift terms. Then, we design balanced schemes…