一类线性变分数阶微分方程的数值解  

Numerical Solutions of a Class of Linear Fractional Differential Equations with Variable Coefficients

作　　者：黄燕萍 Huang Yanping(College of Science and Technology,Guilin University,Guilin,Guangxi 541006)

机构地区：[1]桂林学院理工学院,广西桂林541006

出　　处：《玉林师范学院学报》2024年第3期11-15,共5页Journal of Yulin Normal University

基　　金：广西高校中青年教师科研基础能力提升项目(2021KY1595)

摘　　要：本文主要利用Haar小波方法研究一类变系数线性分数阶微分方程的数值解.首先,将微分方程转化为等价的Volterra积分方程,分析微分方程有解.然后,将Haar小波结合算子矩阵思想得到Haar小波的分数阶微分方程算子矩阵,并将分数阶微分方程的变系数和已知函数离散化,进而变系数线性分数阶微分方程转化为线性代数方程组,得到原方程的数值解,同时验证该算法的收敛性.最后,通过算例说明该算法的有效性和适用性.This paper mainly discusses the numerical solutions of a class of linear fractional differential equations by using Haar wavelet method.The existence of solution of boundary value problem is obtained by using Schauder fixed point theorem.First,the differential equation is transformed into an equivalent integral equation,and the solution of the differential equation is analyzed.Then,the operator matrix of Haar wavelet is obtained by combining Haar wavelet with operator matrix idea,and the variable coefficients and known functions of the fractional differential equations are discretized,and the linear fractional differential equations with variable coefficients are transformed into linear algebraic equations to obtain the numerical solution of the original equation,so the convergence of the algorithm is verified.Finally,an example is given to illustrate the effectiveness and applicability of the proposed algorithm.

关 键 词：分数阶微分方程 HAAR小波 算子矩阵 数值解 

分 类 号：O175.1[理学—数学]