We propose a finite difference scheme for the Heisenberg equation and the LandauLifshitz equation. These equations have a length-preserving property and energy conservation or dissipation property. Our proposed scheme inherits both characteristic properties. We also show that the boundedness of finite difference solutions and an unique solvability of our scheme. Finally, we show some numerical ...

Abstract—This paper presents the heat and mass driven natural convection succession in a Darcy thermally stratified porous medium that embeds a vertical semi-infinite impermeable wall of constant heat flux and concentration. The scale analysis of the system determines the two possible maps of the heat and mass driven natural convection sequence along the wall as a function of the process parame...

Abstract: Complex diffusion is a common and broadly used denoising procedure in image processing. The method is based on an explicit finite difference scheme applied to a diffusion equation with a proper complex diffusion parameter in order to preserve edges and the main features of the image, while eliminating noise. In this paper we present a rigorous proof for the stability condition of comp...

Cheng Wang, Jian-Guo Liu, Hans Johnston 1 Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA; e-mail: [email protected] 2 Institute for Physical Science and Technology and Department of Mathematics, University of Maryland, College Park, MD 20742, USA; e-mail: [email protected] 3 Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA; e-mail: hansjo...

This paper deals with the numerical approximation of the solution of 1D parabolic singularly perturbed problems of reaction–diffusion type. The numerical method combines the standard implicit Euler method on a uniform mesh to discretize in time and a HODIE compact fourth order finite difference scheme to discretize in space, which is defined on a priori special meshes condensing the grid points...

Continuing our investigation of the tRNA genes and gene products in Mycoplasma mycoides, we report the sequence of the gene for tRNALeu (CAA) as well as partial primary structures of the following tRNAs: Leu (CAA), Leu (UAG), Arg (UCU), Thr (AGU) and Ile (CAU). It is suggested that in M. mycoides, at least some of the family codon boxes are read by only one tRNA each, using an unconventional me...

Starting from a high-order local nonreflecting boundary condition (NBC) for single scattering [25], we derive a local NBC for time-dependent multiple scattering problems, which is completely local both in space and time. To do so, we first develop an exterior evaluation formula for a purely outgoing wave field, given its values and those of certain auxiliary functions needed for the local NBC a...

Contents Preface Introduction xv 1 1.1 A one-dimensional model problem 2 1.2 A two-dimensional example of heat propagation in a heterogeneous material 3 1.3 Examples of irregular domains and free boundary problems 5 1.4 The scope of the monograph and the methodology 5 1.4.1 Jump conditions 7 1.4.2 The choice of grids 7 1.5 A minireview of some popular finite difference methods for interface pro...

A (v, k, λ) difference family ((v, k, λ)-DF in short) over an abelian group G of order v is a collection F = {Bi | i ∈ I} of k-subsets of G, called base blocks, such that each nonzero element of G can be represented in precisely λ ways as a difference of two elements lying in some base blocks in F . A disjoint (v, k, λ)-DF is a difference family with disjoint blocks. In this paper, it is proved...