Legendre小波函数求解非线性Volterra积分微分方程组的数值解  

Legendre Wavelet Method for Numerically Solving Nonlinear System of Volterra Integro-Differential Equations

作　　者：朱帅[1] 朱世昕[2] ZHU Shuai;ZHU Shi-xin(School of Mat hematics and Computer Science,Shanxi Datong University,Datong 037009,China;School of Educational Science and Technology,Shanxi Datong University,Datong 037009,China)

机构地区：[1]山西大同大学数学与计算机科学院,山西大同037009 [2]山西大同大学教育科学与技术学院,山西大同037009

出　　处：《数学的实践与认识》2019年第24期202-207,共6页Mathematics in Practice and Theory

基　　金：山西省高等学校科技创新项目(2019L0774)

摘　　要：Legendre小波函数被用于逼近非线性Volterra积分微分方程组的解,方法是基于Legendre小波的性质构建相应的积分算子矩阵,进而将原问题转化为关于未知解系数的线性方程组,通过求解该方程组,即得原问题的数值解.数值结果表明所述方法对于求解此类问题是行之有效的.In this paper,Legendre wavelet method is applied to approximate the solutions of nonlinear system of Volterra integro-differential equations.Then the original problem is reduced to a system of linear algebraic equations regarding the unknown coefficients,the unknown solutions are obtained by solving the system.Lastly the obtained numerical results show that our method is effective and feasible.

关 键 词：LEGENDRE小波 算子矩阵 非线性Volterra积分微分方程组 数值解 

分 类 号：O241.8[理学—计算数学]