无界区域抛物方程自然边界元方法

本文应用自然边界元方法求解无界区域抛物型初边值问题。首先将控制方程对时间进行离散化,得到关于时间步长离散化的椭圆型问题。通过Fourier展开,导出相应问题的自然积分方程和Poisson积分公式。研究了自然积分算子的性质,并讨论了自然积分方程的数值解法,最后给出数值例子。从而解决了抛物型问题的自然边界归化和自然边界元方法。     

二阶非线性微分方程的斜周期边值问题

In this paper a uniqueness theorem for a skewperiodic boundary value problem is obtained. By using the optimal control method, we derive the best estimate for the integration mean ensuring that the results hold.     

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.     

非齐次微分方程两点边值问题正解的存在性及多重性

本文考虑一类非齐次微分方程的两点边值问题,得到了一些有关其正解存在性与多重性的精确条件．     

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.     

泊松类型方程边界元解法

本文采用高阶拉普拉斯算子基本解将泊松类型方程的区域积分全部变换成边界积分，使计算问题的维数减少一维．通过斯托克斯方程的算例，表明本文所用的方法是有效的方法。     

气体放电击穿过程的物理和数值研究

本文对低气压（１０＾－２Ｐａ）热阴极气体放电的击穿过程给出了物理描述和相应的双流体数学型，并发展了一种选择和调整未知初始条件的有效算法，可以通过伴随试射法得到对初始条件十分敏感的非线性两点边值常微分方程组的数值解，从而给出这类气体放电中击穿过程的定量描述。     

水闸闸室结构三维样条边界元分析

用三维样边界元法分析水闸闸室结构。底板，闸墩和载水墙等为其子结构，交通桥，工作桥和胸墙等处理为内部支撑。地基和边载可以是任意的，只要能给定地表位移面力关系。在各种工况下，不论是设置平板门还是弧形门，是平底板是反拱底板，即使在稀疏剖分下也能给出高精度的位移场，应力场和地基反力场。     

A mathematical model of the ring-spinning process

This paper develops a mathematical model of the ring-spinning process that takes into account its non-stationary nature. A complex system of differential equations is obtained, which from a mathematical point of view constitutes a ‘free-boundary’ problem. Its solution involves definition of suitable boundary conditions related to the mechanical characteristics of the process and of the spinning machine itself. The boundary conditions which determine the solution are pointed out. A numerical solution of the system of differential equations can be obtained by the Finite-Segments method, as shown in an example.     

HIGH ACCURACY FINITE VOLUME ELEMENT METHOD FOR TWO-POINT BOUNDARY VALUE PROBLEM OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

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