Numerical solution of differential equations using Sinc method based on the interpolation of the highest derivatives

In general, we will use the numerical differentiation when dealing with the differential equations. Thus the differential equations can be transformed into algebraic equations and then we can get the numerical solutions. But as we all have known, the numerical differentiation process is very sensitive to even a small level of errors. In contrast it is expected that on average the numerical integration process is much less sensitive to errors. In this paper, based on the Sinc method we provide a new method using Sinc method incorporated with the double exponential transformation based on the interpolation of the highest derivatives (SIHD) for the differential equations. The error in the approximation of the solution is shown to converge at an exponential rate. The numerical results show that compared with the exiting results, our method is of high accuracy, of good convergence with little computational efforts. It is easy to treat nonhomogeneous mixed boundary condition for our method, which is unlike the traditional Sinc method.     

Bifurcations of Invariant Tori and Subharmonic Solutions of Singularly Perturbed System

This paper deals with bifurcations of subharmonic solutions and invariant tori generated from limit cycles in the fast dynamics for a nonautonomous singularly perturbed system. Based on Poincare map, a series of blow-up transformations and the theory of integral manifold, the conditions for the existence of invariant tori are obtained, and the saddle-node bifurcations of subharmonic solutions are studied.     

Stabilization of valence fluctuations in the cerium solid by the time-dependent collision approach

The collision-generated hybridization which has been found responsible for the on-site mixing of the atomic-likef-state and the band-liked states in mixed valence solids has been studied for the cerium solid. A practical expression which depends on the lattice constant and temperature has been obtained for the collision-generated hybridization. Numerical calculations show that the valence varies continuously with lattice constant and that temperature makes the transition smoother. The collision-generated hybridization is found to be of significant strength in the intermediate valence regime; but over a wide range of the valence near 3.5 it varies rather slowly without preferring a particular valence. Factors which can assist the collision-generated hybridization in stabilizing the mixed valence phase at a particular lattice constant are discussed.     

线性规划问题的一种新的摄动法

在用单纯形方法解线性规划的问题时，不可避免会出现退化情况，而某些退化情况会导致循环。目前采用的避免循环的方法一共有两类：传统的摄动法（字典序）和Bland方法。本分析了传统摄动法的一些不足，给出了一种新的摄动法。     

一类过程摄动系统的无阻塞鲁棒性

使用参数Dioid模块网络法,把含大量摄动参数的在普通极大代数意义下非线性状态空间模型在参数Dioid意义下线性化,在此基础上研究一类过程摄动系统的无阻塞鲁棒性.给出了有限缓冲串行生产系统在没有缓冲器下无阻塞的充要条件和充分条件.     

New initial-value method for singularly perturbed boundary-value problems

An initial-value method is given for second-order singularly perturbed boundary-value problems with a boundary layer at one endpoint. The idea is to replace the original two-point boundary value problem by two suitable initial-value problems. The method is very easy to use and to implement. Nontrivial text problems are used to show the feasibility of the given method, its versatility, and its performance in solving linear and nonlinear singularly perturbed problems.This work was supported in part by the Consiglio Nazionale delle Ricerche, Contract No. 86.02108.01, and in part by the Ministero della Pubblica Istruzione.     

An Alternative Approach to Obtain the Exact Wave Functions of Time-Dependent Hamiltonian Systems Involving Quadratic, Inverse Quadratic, and (1/x)p+p(1/x) Terms

By using the Lewis-Riesenfeld theory and algebraic method, we present an alternative approach to obtain the exact solution of time-dependent Hamiltonian systems involving quadratic, inverse quadratic and (1/x)p+p(1/x) terms. This solution is discussed and compared with that obtained by Choi, J. R. (2003). International Journal of Theoretical Physics 42, 853]. PACS: 03.65Ge; 03.65Fd; 03.65Bz     

Martin Boundaries of Elliptic Skew Products, Semismall Perturbations, and Fundamental Solutions of Parabolic Equations

We consider positive solutions of elliptic partial differential equations on non-compact domains of Riemannian manifolds. We explicitly determine Martin boundaries and Martin kernels for a class of elliptic equations in skew product form by exploiting and developing perturbation theory for elliptic equations and short/long-time estimates for fundamental solutions of parabolic equations.     

四阶半线性椭圆型积分微分方程的奇摄动

本文研究了一个四阶椭圆型积分微分方程的奇摄动问题。证明了相应的比较定理并得到了解的一致有效的渐近展开式。     

四阶微分方程三点边值问题的奇摄动

该文用Ｓｈａｕｄｅｒ不动点定理及微分不等式理论研究了一类非线性四阶常微分方程三点边值问题的存在性，并利用边界层校正法获得解及其二阶导数的高阶渐进展开式．