一种非光滑函数的二阶梯度微分方程求解算法  

An Algorithm for Solving Second-order Gradient Differential Equations with Nonsmooth Functions

作　　者：姚爱娣 王林 YAO Aidi;WANG Lin(School of Mathematics and Big Data,Anhui University of Science and Technology,Huainan 232001,China)

机构地区：[1]安徽理工大学数学与大数据学院,安徽淮南232001

出　　处：《太原师范学院学报（自然科学版）》2021年第2期25-29,共5页Journal of Taiyuan Normal University:Natural Science Edition

基　　金：安徽省高等学校省级教学示范课复变函数(示范课)(13210412).

摘　　要：为了更好地解决复杂非线性多目标模型求解问题,提出一种非光滑函数的二阶梯度微分方程求解算法.结合非光滑函数针对二阶梯度微分方程中的凸函数性质进行分析和演化,规范凸函数的一阶和二阶性质定义,从而求解常微分方程和偏微分方程.进一步根据非光滑函数的基本原理,对非光滑函数导数进行求解,并对非光滑函数的二阶梯度微分方程的误差数值进行检测和修正,保证二阶梯度微分方程求解算法的有效性同时提高算法的防滑性能,最后通过对比实验证实了非光滑函数的二阶梯度微分方程求解算法在实际应用过程中的可行性.In order to solve the complex nonlinear multi-objective model better,a second-order gradient differential equation algorithm with non-smooth functions is presented.The properties of convex functions in second-order gradient differential equations are analyzed and evolved with Nonsmooth functions.The first and second properties of convex functions are defined to solve ordinary and partial differential equations.Based on the basic principle of non-smooth function,the derivative of non-smooth function is solved,and the error values of the second-order gradient differential equation of non-smooth function are detected and corrected to ensure the effectiveness of the second-order gradient differential equation solving algorithm and improve the anti-slip performance of the algorithm.Finally,the feasibility of the second-order gradient differential equation solving algorithm for non-smooth functions in practical application is verified by comparative experiments.

关 键 词：非光滑函数 二阶梯度 微分方程 

分 类 号：O343[理学—固体力学]