奇异高阶微分方程的边界值确定方法研究

发布时间：2018-03-17 20:48

本文选题：奇异高阶微分方程　切入点：边界值　出处：《科技通报》2017年09期 　论文类型：期刊论文

【摘要】：针对在确定奇异高阶微分方程的边界值时,一直存在边界值确定不准确等问题。本文对奇异高阶微分方程进行研究,深入研究方程边界值确定方法。首先,考虑奇异三点边值问题,构建边值问题的Green函数,根据Green函数的性质描述高阶微分方程解的导函数性质,获取奇异微分方程存在特征值,利用单元中心差分法计算算子奇异问题方程数据,确定奇异积分Hermite三角插值,通过对方程单元中心差分理论将函数离散点进行重构,对连续桉树的固定节点值做收敛性分析,通过给定误差估计确定边界值。实验分析结果表明,所提奇异高阶微分方法对其边界值能够高精度确定,对微分方程分析具有重要意义。
[Abstract]:In order to solve the problem of inaccuracy in determining the boundary value of singular higher order differential equations, this paper studies the singular higher order differential equations, and studies the method of determining the boundary value of the singular higher order differential equations. First, the method of determining the boundary value of the singular higher order differential equations is studied. Considering the singular three-point boundary value problem, the Green function of the boundary value problem is constructed. According to the properties of the Green function, the differential function property of the solution of the higher order differential equation is described, and the existence eigenvalue of the singular differential equation is obtained. The singular integral Hermite trigonometric interpolation is determined by using the element central difference method to calculate the equation data of operator singular problem. The discrete point of the function is reconstructed by the central difference theory of the equation unit, and the convergence of the fixed node value of continuous eucalyptus tree is analyzed. The experimental results show that the singular high-order differential method can be used to determine the boundary value with high accuracy and is of great significance to the analysis of differential equations.
【作者单位】：山西警察学院;
【分类号】：O175.8

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