在再生核空间中求解非线性奇异两点边值问题

数学物理学报 ›› 2009, Vol. 29 ›› Issue (5): 1274-1282.

在再生核空间中求解非线性奇异两点边值问题

哈尔滨师范大学数学科学学院信息科学系哈尔滨 150025 哈尔滨工业大学理学院数学系哈尔滨 150001

收稿日期:2007-09-25 修回日期:2008-11-10 出版日期:2009-10-25 发布日期:2009-10-25
基金资助:
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

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

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

摘要/Abstract

摘要：

该文建立了一个迭代方法求解一类奇异两点边值问题(x_αu')'=f (x, u, u'), 其中x ∈ (0,1), α< 2. 解的表达式是在再生核空间W₂[0,1]中以级数的形式给出的. 近似解一致收敛到准确解. 并且, 误差是单调下降的. 最后通过一些数值算例论述了所提方法的正确性与有效性.

关键词: 准确解, 奇异两点边值问题, 再生核空间

Abstract:

In this paper, the authors establish an iterative method to compute solution for a class of singular two-point boundary value problems (x^αu')'=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 u_n(x) is proved to converge to the exact solution. Furthermore, the approximate error of u_n(x) is monotone decreasing. Some numerical examples are illustrated to demonstrate the accuracy of the present method.

中图分类号:

34B16

吕学琴, 崔明根. 在再生核空间中求解非线性奇异两点边值问题[J]. 数学物理学报, 2009, 29(5): 1274-1282.

LV Xue-Qin, CUI Ming-Gen. Solving Nonlinear Singular Two-point Boundary-value Problem in the Reproducing Kernel Space[J]. Acta mathematica scientia,Series A, 2009, 29(5): 1274-1282.

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