奇异高阶微分方程的边界值确定方法研究

Study on Boundary Value Determination of Singular Higher Order Differential Equations

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。

For the determination of boundary value of singular high order differential equations,theboundary value determination problem is always inaccurate.In this paper,we study the singular higherorder differential equations,and study the method of determining the boundary value of the equations.First,consider the singular three point boundary value problems,constructing the Green function of theboundary value problem,according to the properties of the Green function to describe the properties ofderivative of higher order differential equations,singular differential equations are obtained bycalculating the eigenvalues,singular problem equation according to difference by the unit center,determine the singular integral Hermite trigonometric interpolation,by the central difference equation ofelement theory to reconstruct the function of discrete points,fixed nodes of continuous Eucalyptus valueconvergence analysis,through the given error estimation for the boundary value to achieve.Theexperimental results show that the proposed high order differential method can determine the boundaryvalue of the system with high accuracy.It is of great significance to differential equation analysis.