Exponential sum approximation for Mittag-Leffler function and its application to fractional Zener wave equation
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
Author(s)
Related Research Unit(s)
Detail(s)
Original language | English |
---|---|
Article number | 109389 |
Journal / Publication | Journal of Computational Physics |
Volume | 410 |
Online published | 9 Mar 2020 |
Publication status | Published - 1 Jun 2020 |
Link(s)
Abstract
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 (T2 ), where T is the interval each time step, provided that the approximation error of the MLF is sufficiently small.
Research Area(s)
- Fast convolution, Finite element method, Fractional calculus, Gaussian quadrature, Mittag-Leffler function, Stability analysis
Citation Format(s)
Exponential sum approximation for Mittag-Leffler function and its application to fractional Zener wave equation. / Lam, P. H.; So, H. C.; Chan, C. F.
In: Journal of Computational Physics, Vol. 410, 109389, 01.06.2020.
In: Journal of Computational Physics, Vol. 410, 109389, 01.06.2020.
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review