Exponential sum approximation for Mittag-Leffler function and its application to fractional Zener wave equation
Mittag-Leffler函数的指数和逼近及其在分数阶齐纳波方程中的应用
 作者： P.H. Lam,  H.C. So,  C.F. Chan 作者单位： 1Department of Electrical Engineering, City University of Hong Kong, Kowloon, Hong Kong Special Administrative Region 刊名： Journal of Computational Physics, 2020, Vol.410 来源数据库： Elsevier Journal DOI： 10.1016/j.jcp.2020.109389 关键词： Fractional calculus;  Mittag-Leffler function;  Gaussian quadrature;  Finite element method;  Fast convolution;  Stability analysis; 原始语种摘要： Abstract(#br)The Mittag-Leffler function (MLF) is fundamental to solving fractional calculus problems. An exponential sum approximation for the single-parameter MLF with negative input is proposed. Analysis shows that the approximation, which is based on the Gauss-Legendre quadrature, converges uniformly for all non-positive input. The application to modelling of wave propagation in viscoelastic material with the finite element method is also presented. The propagation speed of the solution to the approximated wave equation is proved to have the same upper bound as the original. The discretized scheme, based on the generalised alpha method, involves only a single matrix inverse whose size is the degree of freedom of the geometric model per time step. It is proved that the scheme is... unconditionally stable. Furthermore, the solution converges to the true solution at O ( T 2 ) , where T is the interval each time step, provided that the approximation error of the MLF is sufficiently small.

• approximation　近似
• fractional　分级的
• application　申请
• convolution　褶积
• function　函数
• exponential　指数的
• geometric　凡何
• proved　证实储量
• equation　方程
• fundamental　基本的