| 一类弱奇异边值问题的大范围收敛算法 |
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| 引用本文： | 周永芳,崔明根.一类弱奇异边值问题的大范围收敛算法[J].数学物理学报(A辑),2011,31(1):142-153. |
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| 作者姓名： | 周永芳 崔明根 |
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| 作者单位： | 1.哈尔滨工业大学数学系 哈尔滨 150001|2.黑龙江科技学院数力系 哈尔滨 150027 |
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| 基金项目： | 黑龙江省自然科学基金(A201015)和黑龙江省教育厅科学技术研究项目(11541323)资助 |
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| 摘 要： | 该文研究如下的弱奇异边值问题: (p(x)y')'=f(x, y),0b0g(x), 0≤b0<1, 边值条件为y(0)=A,αy(1)+β y'(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1]. 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.
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| 关 键 词： | 奇异边值问题 迭代方法 解的存在性 再生核空间 |
| 收稿时间： | 2008-11-08 |
| 修稿时间： | 2010-03-03 |
A Kind of Large-range Convergence Algorithm for Weakly Regular Singular Boundary Value Problems |
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| Zhou Yongfang,Cui Minggen.A Kind of Large-range Convergence Algorithm for Weakly Regular Singular Boundary Value Problems[J].Acta Mathematica Scientia,2011,31(1):142-153. |
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| Authors: | Zhou Yongfang Cui Minggen |
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| Institution: | 1.Department of Mathematics, Harbin Institute of Technology, Harbin 150001|2.Heilongjiang Institute of Science and Technology, Harbin |150027 |
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| Abstract: | In this paper, the weakly regular singular boundary value problem (p(x)y')'=f(x, y), 0<≤1, with p(x)=xb0g(x), 0≤b0<1, and the boundary conditions y(0)=A, αy(1)+β y'(1)=γ, or y'(0)=0, αy(1)+βy'(1)=γ(R.K. Pandey and Arvind K. Singh presented the second order finite
difference methods1] 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. |
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| Keywords: | Singular boundary value problemzz Iterative methodzz Existence of solutionzz Reproducing kernel spacezz |
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