一类弱奇异边值问题的大范围收敛算法

A Kind of Large-range Convergence Algorithm for Weakly Regular Singular Boundary Value Problems

该文研究如下的弱奇异边值问题:(p(x)y')'=f(x,y),0<x≤1,带有初值条件为p(x)=x^(b_0)g(x),0≤b_0<1,边值条件为y(0)=A,αy(1)+βy'(1)=γ或y'(0)=0,αy(1)+βy'(1)=γ(R.K.Pandey和Arvind K.Singh给出了一种求解此问题的二阶有限差分方法.在再生核空间中讨论方程解的存在性,给出一种新的迭代算法,这种迭代算法是大范围收敛的.给出数值算例并与R.K.Pandey和Arvind K.Singh给出的方法进行比较说明该文方法的有效性.

In this paper,the weakly regular singular boundary value problem（p（x）y＇）＇ = f（x,y）,0x≤1,with p（x） = x^（b_0）g（x）,0≤b_01,and the boundary conditions y（0） = A,αy（1） ＋βy＇（1） =γ,or y＇（0） = 0,αy（1） ＋βy＇（1） =γ（R.K.Pandey and Arvind K.Singh presented the second order finite difference methods is considered.The existence of the solution and a new iterative algorithm which is large-range convergent are established for the problems in reproducing kernel space.Illustrative examples are included to demonstrate the validity and applicability of the technique through comparing the method with the method given by R.K.Pandey and Arvind K.Singh.