# 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

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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.

 [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.