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
楼钦艺 1许小勇 1何通森 1朱婷1
作者信息
- 1. 东华理工大学理学院,330013,南昌
- 折叠
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.
Abstract
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 equa-tion 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Key words
higher order Haar wavelet/Caputo-Fabrizio derivative/ordinary differential equation/collocation method引用本文复制引用
基金项目
江西省自然科学基金(2020BABL201006)
东华理工大学博士科研基金(DKBK2019213)
出版年
2024
国家科技期刊平台
NSTL
万方数据