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
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。
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.
参考文献
|
[1]
|
Henderson, J. and C.J. Kunkel (2008) Uniqueness of Solutions of Linear Nonlocal Boundary Value Problems. Applied Mathematics Letters, 21, 1053-1056.
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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