高阶Haar小波方法求解一类Caputo-Fabrizio分数阶微分方程  

Numerical Solution of A Class of Caputo-Fabrizio Fractional-order Differential Equations Using Higher Order Haar Wavelet Method

作　　者：楼钦艺 许小勇 何通森 朱婷 LOU Qinyi;XU Xiaoyong;HE Tongsen;ZHU Ting(School of Science,East China University of Technology,330013,Nanchang,PRC)

机构地区：[1]东华理工大学理学院,南昌330013

出　　处：《江西科学》2024年第3期470-474,519,共6页Jiangxi Science

基　　金：江西省自然科学基金项目(2020BABL201006);东华理工大学博士科研基金项目(DKBK2019213)。

摘　　要：利用高阶Haar小波配置法求解了一类Caputo-Fabrizio分数阶微分方程。通过Caputo-Fabrizio分数阶积分将原方程转化为等价的二阶常微分方程,再结合高阶Haar小波配置法将得到的常微分方程化为线性代数方程组进行求解。数值实验表明,使用很小的尺度J可以得到满意的数值精度,且增加尺度J可以获得更高精度的数值解,该算法稳定,具有一定的应用价值。Higher order Haar wavelet collocation method is used to solve a class of Caputo-Fabrizio fractional differential equations.Through Caputo-Fabrizio fractional integration,the original equation is transformed into an equivalent second order ordinary differential equation,and then combined with higher order Haar wavelet collocation method,the obtained ordinary differential equation is transformed into a system of linear algebra equations.Numerical experiments have shown that using a very small scale J can achieve satisfactory numerical results,and increasing the scale J can obtain the numerical solutions with higher accuracy.The algorithm is stable and has some application value.

关 键 词：高阶Haar小波 Caputo-Fabrizio导数 常微分方程 配置法 

分 类 号：O241.81[理学—计算数学]