AAM  >> Vol. 6 No. 8 (November 2017)

    高阶非线性微分方程非局部边值问题的解法
    Solving Higher Order Nonlinear Differential Equation with Nonlocal Boundary Value Problem

  • 全文下载: PDF(309KB) HTML   XML   PP.1034-1038   DOI: 10.12677/AAM.2017.68124  
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作者:  

周永芳,马丽君,张相梅,金大永,苏国忠:河北工业大学理学院,天津

关键词:
非局部边值问题高阶非线性微分方程再生核空间Nonlocal Boundary Value Problems Higher Order Nonlinear Differential Equation Reproducing Kernel Space

摘要:

本文讨论高阶非线性微分方程非局部边值问题的数值方法。通过建立满足非局部边值条件的再生核空间,获得简单易行的再生核数值解法。证明近似解及其导数的收敛性。

This paper discusses the numerical method for the higher order nonlinear differential equation with nonlocal boundary value problem. By constructing the reproducing kernel space which satis-fies the nonlocal boundary value conditions, the simple reproducing kernel numerical approximate method is established. Convergence of approximate solution and its derivatives is proved, respectively.

文章引用:
周永芳, 马丽君, 张相梅, 金大永, 苏国忠. 高阶非线性微分方程非局部边值问题的解法[J]. 应用数学进展, 2017, 6(8): 1034-1038. https://doi.org/10.12677/AAM.2017.68124

参考文献

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[2] Henderson, J. (2011) Ex-istence and Uniqueness of Solutions of (k+2)-Point Nonlocal Boundary Value Problems for Ordinary Differential Equations. Nonlinear Analysis: Theory, Methods & Applications, 74, 2576-2584.
https://doi.org/10.1016/j.na.2010.11.048
[3] Henderson, J. and Luca, R. (2012) Existence and Multiplicity for Positive Solutions of a Multi-Point Boundary Value Problem. Applied Mathematics and Computation, 218, 10572-10585.
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[4] 周永芳. 若干微分方程非局部边值问题的一种数值方法[D]: [博士学位论文]. 哈尔滨: 哈尔滨工业大学, 2011: 15-19.