Haar小波方法求解一类耦合分数阶积分微分方程组数值解  

Numerical Solutions of a Class of Coupled Fractional Integral-Differential Equations Utilizing Haar Wavelet Scheme

作　　者：袁桂蓉[1] 张艳波[2] 贾文燕 YUAN Gui-rong;ZHANG Yan-bo;JIA Wen-yan(Chongqing Electric Power College,Chongqing 400053,China;School of Information Engineering,Tarim University,Alear 843300,China;School of Education,Zhengzhou Sias College,Zhengzhou 451150,China)

机构地区：[1]重庆电力高等专科学校,重庆400053 [2]塔里木大学信息工程学院,新疆阿拉尔843300 [3]郑州西亚斯学院教育学院,河南郑州451150

出　　处：《数学的实践与认识》2020年第20期243-249,共7页Mathematics in Practice and Theory

基　　金：河南省科技攻关项目(072102230007)。

摘　　要：利用Haar小波正交函数方法求解一类耦合的二维分数阶积分微分方程组.首先给出了Haar小波函数以及Riemann-Liouville分数阶积分和Caputo分数阶微分定义,然后将待求解问题中的解函数和已知二元函数由Haar小波正交级数近似表示,进而通过引入Haar小波分数阶积分算子矩阵将待求问题表示成一些向量或矩阵的乘积,最后离散未知变量获得原问题的数值解.最后通过一些具体的测试算例对算法的有效性及可行性进行了验证.In this paper,the orthogonal Haar wavelet function is used to solve a class of coupled two-dimensional fractional integraldifferential equations.Firstly,this paper presents the Haar wavelet function and RiemannLiouville fractional integral and Caputo fractional differential definition.Then the solution function and arbitrary two-variables known functions are approximated by Haar wavelet orthogonal series.Furthermore with the introduction of fractional integral operational matrices of Haar wavelet functions,the original system is transferred into some products of vectors or matrices.Lastly the numerical solutions of the original problem are acquired by dispersing unknown variables.In addition,the validity and feasibility of the algorithm are verified by some concrete test examples.

关 键 词：HAAR小波 积分微分方程组 算子矩阵 分数阶 数值解 

分 类 号：O241.8[理学—计算数学]