Exponential sum approximation for Mittag-Leffler function and its application to fractional Zener wave equation
作者: P.H. LamH.C. SoC.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 calculusMittag-Leffler functionGaussian quadratureFinite element methodFast convolutionStability 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...
全文获取路径: Elsevier  (合作)
影响因子:2.138 (2012)

  • 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