Application of the method of lines to unsteady compressible Euler equations

In the sense of method of lines, numerical solution of the unsteady compressible Euler equations in 1D, 2D and 3D is split into three steps: First, space discretization is performed by the first‐order finite volume method using several approximate Riemann solvers. Second, smoothness and Lipschitz continuity of RHS of the arising system of ordinary dimensional equations (ODEs) is analysed and its solvability is discussed. Finally, the system of ODEs is integrated in time by means of implicit and explicit higher‐order adaptive schemes offered by ODE packages ODEPACK and DDASPK, by a backward Euler scheme based on the linearization of the RHS and by higher‐order explicit Runge–Kutta methods. Time integrators are compared from several points of view, their applicability to various types of problems is discussed, and 1D, 2D and 3D numerical examples are presented. Copyright © 2003 John Wiley & Sons, Ltd.     

Positive unbounded solutions of second order quasilinear ordinary differential equations and their application to elliptic problems

In this paper we consider positive unbounded solutions of second order quasilinear ordinary differential equations. Our objective is to determine the asymptotic forms of unbounded solutions. An application to exterior Dirichlet problems is also given.     

滚刀的现场试验及数学模型

本文分析了现有滚刀耐用度公式之不足,采用含有刀具磨损量的广义泰勒公式为数学模型,结合生产现场进行滚刀耐用度试验,所得结果更具有普遍意义。     

EXISTENCE OF PERIODIC SOLUTION FOR HIGHER ORDER NONLINEAR DIFFERENTIAL EQUATION

The existence of periodic solutions is proved for the higher order nonlinear differential equation by applying Leray-Schauder principle and Wirtinger's inequality.     

普通车床常见故障的分析与排除

分析了造成普通车床常见故障的原因,总结了故障排除和检修的主要方法,对普通车床及其相关机床的使用、维护和检修具有一定的借鉴和参考价值。     

New Explicit Exact Solutions of the Born–Infeld Equation

By introducing an auxiliary ordinary differential equation and solving it by means of the method of separation of variables, many new explicit exact solutions to the Born–Infeld equation are found in a concise manner. PACS: 02.30.Jr; 03.40.Kf     

关于具有转点的常微分方程的边值问题

本文研究下面形式的边值问题εy″-f(x,ε)y′ g(x,ε)y=0 (-α≤x≤b,0<ε≤1)y(-α)=α,y(b)=β其中f(x,0)在区间[-a,b]上具有多个和多重零点.给出了出现边界层和内部层的条件,并在相应的条件下,构造解的渐近展开式.     

一个反应扩散系统解的周期渐近性态

证明了一个二维反应扩散系统,当扩散系数相等且充分大时,其整体正解或趋于系统的正常数平衡解,或趋于一个空间齐次周期解的渐近结果.