On Stability of Negative Index Singular Integral Equations over an Interval

By normalization of the negative index singular integral equations with Cauchy kernel over (-1,1), the stability of the equations is proved, and the error estimate of the perturbed solutions is precisely investigated. Submitted: September 5, 2000? Revised: December 6, 2001.     

一类奇性积分方程的多尺度配置快速算法

This paper develops fast multiscale collocation methods for a class of Fredholm integral equations of the second kind with singular kernels. A truncation strategy for the coefficient matrix of the corresponding discrete system is proposed, which forms a basis for fast algorithms. The convergence, stability and computational complexity of these algorithms are analyzed.     

两类无界域边界上的奇异积分方程

给出两类无界域边界上完全奇异积分方程的直接解法．方程的系数和核密度在该无异域上具某种解析性．     

广义Hammerstain型非线性奇异积分方程的可解性定理

本文所讨论的广义Hammerstain型非线性奇异积分方程:(*)是以流体弹性力学和断裂力学的边值问题为背景。我们分别对k>0,k=0,k<0这三种情况研究了方程(＊)的可解性,用Newton-Kantorovic方法和Banach不动点原理证明了方程(*)在不同条件下解的存在唯一性定理,从而推广了的工作。     

L~1空间中弱奇性积分方程特征值的数值解法探究

在L¹空间中讨论弱奇性积分方程的特征值问题,给出了一种算法,证明所提出算法的合理性,并举出具体算例,通过Matlab编程算出所给算例的近似数值解.     

一般形式的奇异对偶积分方程组正交多项式求解法

基于Jacobi正交多项式法,直接求解一般形式的对偶积分方程组,将对偶积分方程组中的未知函数,表示成n次Jacobi正交多项式级数,用正交多项式将奇异对偶积分方程组,化成线性代数方程组,通过求解级数中的各项系数,由此给出奇异对偶积分方程组的一般性解,并严格证明了奇异对偶积分方程组和由它化成的线性代数方程组的等价性,解的存在性和解的表示形式不唯一性．本文给出的理论解和解法,可供求解复杂的数学、物理、软科学中的混合边值问题应用．     

Initial Value Problem for a Nonlinear Evolution System with Singular Integral Differential Terms

The initial value problem for a nonlinear evolution system with singular integral differential terms is studied. Dy means of a priori estimates of the solutions and Lcray-Schauder's fixed point theorem, we demonstrate the existence and uniqueness theorems of the generalized and classical global solutions to the problem.     

一类对偶积分方程组正则化为Cauchy奇异积分方程组解法

本文基于Mellin变换法求解复杂更一般形式的对偶积分方程组．通过积分变换，由实数域化成复数域上的方程组，引入未知函数的积分变换，移动积分路径，应用Cauchy积分定理，实现退耦正则化为Cauchy奇异积分方程组，由此给出一般性解，并严格证明了对偶积分方程组退耦正则化为Cauchy奇异积分方程组与原对偶积分方程组等价性，以及对偶积分方程组解的存在性和唯一性．给出的解法和理论解，作为求解复杂对偶积分方程组一种有效解法，可供求解复杂的数学、物理、力学中的混合边值问题应用．     

One-dimensional Singular Integral Equations

A class of singular integral equations having solution in closed form is considered. This class contains the characteristic equation and other equations associated with it. Equations are solved by their reduction to some Riemann boundary value problems in generalized Hölder spaces H_φ (Γ), where Γ is a closed rectifiable Jordan curve for which the Plemelj–Privalov theorem holds.