Acta mathematica scientia,Series A ›› 2011, Vol. 31 ›› Issue (1): 142-153.

• Articles • Previous Articles     Next Articles

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

 ZHOU Yong-Fang1,2, CUI Ming-Gen1   

  1. 1.Department of Mathematics, Harbin Institute of Technology, Harbin 150001|2.Heilongjiang Institute of Science and Technology, Harbin |150027
  • Received:2008-11-08 Revised:2010-03-03 Online:2011-02-25 Published:2011-02-25
  • Supported by:

    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

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)=Aαy(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 methods[1] 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.

Key words: Singular boundary value problem, Iterative method, Existence of solution, Reproducing kernel space

CLC Number: 

  • 34B16
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