Nonstandard perturbation approximation and travelling wave solutions of nonlinear reaction diffusion equations

This paper deals with the construction of a nonstandard numerical method to compute the travelling wave solutions of nonlinear reaction diffusion equations at high wave speeds. Related general properties are studied using the perturbation approximation. At high wave speed the perturbation parameter approaches to zero and the problem exhibits a multiscale character. That is, there are thin layers where the solution varies rapidly, while away from these layers the solution behaves regularly and varies slowly. Most of the conventional methods fail to capture this layer behavior. Thus, the quest for some new numerical techniques that may handle the travelling wave solutions at high wave speeds earns relevance. In this paper, one such parameter robust nonstandard numerical scheme is constructed, in the sense that its numerical solution converges in the maximum norm to the exact solution uniformly well for all finite wave speeds. To overcome the difficulty due to the nonlinearity, the problem is linearized using the quasilinearization process followed by nonstandard finite difference discretization. An extensive amount of analysis is carried out which uses a suitable decomposition of the error into smooth and singular component and a comparison principle combined with appropriate barrier functions. The error estimates are obtained, which ensures uniform convergence of the method. A set of numerical experiment is carried out in support of the predicted theory that validates computationally the theoretical results. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

两两NQD列加权和的安全收敛性

本文研究两两NQD系加权和的完全收敛性，证明了一般双下标加权系数的加权部分和的完全收敛性，改进了吴群英（2002）的结果。     

从Stolz定理到L′Hospital法则

给出了从Stolz定理到L′Hospital法则的推导过程及各定理之间的联系.     

Unstructured-grid finite-volume discretization of the Navier-Stokes equations based on high-resolution difference schemes

An unstructured-grid discretization of the Navier-Stokes equations based on the finite volume method and high-resolution difference schemes in time and space is described as applied to fluid dynamics problems in two and three dimensions. The control volume is defined as the cell-vertex median dual control volume. The fluxes through the faces of internal and boundary control volumes are written identically, which simplifies their software implementation. The gradient and the pseudo-Laplacian are calculated at the midpoint of a control volume face by using relations adapted to the computations on a strongly stretched grid in the boundary layer.     

Quantitative determination of acyclovir in plasma by near infrared spectroscopy

The aim of this study was to assess the feasibility of near infrared spectroscopy (NIRS) for analysis of acyclovir in plasma. This methodology was based on the direct measurement of the transmission spectra of liquid samples and a multivariate calibration model (partial least squares, PLS) to determine the acyclovir concentration in plasma sample. The PLS calibration set was built on using the spiked samples by mixing different amounts of acyclovir. Concentration of acyclovir in the plasma samples was calculated employing a 6-factors PLS calibration using the spectral information in the range of 6102-5450 cm^− 1. The root mean square errors of prediction (RMSEP) found was 1.21 for acyclovir. The developed PLS-NIRS procedure allows the determination of 120 samples/h does not require any sample pretreatment and avoids waste generation.     

Fixed-bed drying simulation of agricultural products using a new backward finite difference scheme

This work is concerned with the numerical simulation of fixed-bed corn drying using MSU (Michigan State University) drying model. The classical numerical procedure for MSU model relies on an explicit method of finite differences which requires certain stability conditions between the step sizes of the time and space variables. The objective of the present paper is to establish a stable implicit method based on backward finite differences, in both time and space variables, which takes into account some specific empirical aspects of the problem. Computational results illustrate the efficiency and the flexibility of method.     

Locally one-dimensional difference schemes for the fractional order diffusion equation

Locally-one-dimensional difference schemes for the fractional diffusion equation in multidimensional domains are considered. Stability and convergence of locally one-dimensional schemes for this equation are proved.     

On Appell sequences of polynomials of Bernoulli and Euler type

A construction of new sequences of generalized Bernoulli polynomials of first and second kind is proposed. These sequences share with the classical Bernoulli polynomials many algebraic and number theoretical properties. A class of Euler-type polynomials is also presented.     

Structure relations for monic orthogonal polynomials in two discrete variables

In this paper, extensions of several relations linking differences of bivariate discrete orthogonal polynomials and polynomials themselves are given, by using an appropriate vector–matrix notation. Three-term recurrence relations are presented for the partial differences of the monic polynomial solutions of admissible second order partial difference equation of hypergeometric type. Structure relations, difference representations as well as lowering and raising operators are obtained. Finally, expressions for all matrix coefficients appearing in these finite-type relations are explicitly presented for a finite set of Hahn and Kravchuk orthogonal polynomials.     

A discrete eigenfunctions method for computing mixed hyperbolic problems based on an implicit difference scheme

In this paper numerical solutions of mixed hyperbolic problems are computed using a discrete eigenfunctions method combined with an implicit difference scheme. This new numerical technique preserves the qualitative properties of the analytic solution due to the Sturm-Liouville structure of the underlying discrete linear boundary-value problem and has computational stability advantages vs other methods. Illustrative examples are included.