Acta mathematica scientia,Series A ›› 2009, Vol. 29 ›› Issue (5): 1274-1282.

• Articles • Previous Articles     Next Articles

Solving Nonlinear Singular Two-point Boundary-value Problem in the Reproducing Kernel Space

  

  1. Department of Information Science, School of Mathematica Sciences, Harbin Normal University,  Harbin 150025|Department of Mathematics, School of Science, Harbin Institute of Technology, Harbin 150001
  • Received:2007-09-25 Revised:2008-11-10 Online:2009-10-25 Published:2009-10-25
  • Supported by:

    黑龙江省自然科学基金项目(A2007-11)、哈尔滨师范大学骨干教师资助计划项目(KG2007-03)、哈尔滨师范大学青年学术骨干资助计划项目、哈尔滨师范大学科技发展预研项目(08XYG-13)、黑龙江省新世纪高等教育教学改革工程项目(S08-15)和黑龙江省教育厅项目资助

Abstract:

In this paper, the authors establish an iterative method to compute solution for a class of singular two-point boundary value problems (xαu')'=f(x, u, u'), where x ∈(0,1), and α< 2. Representation of the solution is given in the form of series in the reproducing kernel space W2[0,1]. The n-term approximation un(x) is proved to converge to the exact solution. Furthermore, the approximate error of un(x) is monotone decreasing. Some numerical examples are illustrated  to demonstrate the accuracy of the present method.

CLC Number: 

  • 34B16
Trendmd