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

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。

Abstract: 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 (2017) 高阶非线性微分方程非局部边值问题的解法。 应用数学进展, 6, 1034-1038. doi: 10.12677/AAM.2017.68124

参考文献

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https://doi.org/10.1016/j.aml.2006.06.024

[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.
https://doi.org/10.1016/j.amc.2012.04.019

[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.

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