四阶时间分数波方程的快速紧致差分方法  

A Fast Compact Difference Method for Fourth-Order Time Fractional Wave Equations

作　　者：王婉 张海湘 杨雪花 WANG Wan;ZHANG Haixiang;YANG Xuehua(College of Science,Hunan University of Technology,Zhuzhou Hunan 412007,China)

机构地区：[1]湖南工业大学理学院,湖南株洲412007

出　　处：《湖南工业大学学报》2024年第3期96-101,共6页Journal of Hunan University of Technology

基　　金：国家自然科学基金数学天元基金资助项目(12226340,12226337,12126321);湖南省自然科学基金资助项目(2022JJ50083);湖南省教育厅优秀青年基金资助项目(21B0550)。

摘　　要：对于四阶时间分数波方程,提出了一种快速紧致有限差分方法。该方法对时间Caputo导数采用H2N2方法进行离散,同时为了增加计算效率,采用了指数和来近似核t1-γ,并运用降阶法和差分法对空间导数项进行离散。并证明了该格式的收敛性,得出的空间收敛阶达到四阶,时间收敛阶达到了(3-γ)阶。最后,以数值算例验证了理论分析的有效性,得知该方法所需的CPU时间较短。A fast compact finite difference method,which discretizes the time Caputo derivative by using the H2N2 method,is proposed for fourth-order time fractional wave equations.In view of an increase of the computational efficiency,the exponential sum is used to approximate the kernel t1-γ,with the order reduction method and difference method adopted to discretize the spatial derivative term,thus proving the convergence of the scheme,with a spatial convergence order of four and a temporal convergence order of(3-γ).Finally,numerical examples are used to verify the effectiveness of the theoretical analysis,and it is found that the CPU time required for this method is relatively short.

关 键 词：计算数学 快速算法 H2N2算法 紧致差分方法 

分 类 号：O242.2[理学—计算数学]