首页|Mittag-Leffler Interpolation Integrator for the Time-Fractional Allen–Cahn Equation
Mittag-Leffler Interpolation Integrator for the Time-Fractional Allen–Cahn Equation
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NETL
NSTL
Springer Nature
Abstract In this paper, a fully discrete scheme is presented for solving the time-fractional Allen–Cahn equation. The proposed scheme exhibits superlinear convergence in time. The space discretization is performed using the spectral Galerkin method. The time discretization is designed by combining the Mittag-Leffler function representation of the solution, the integrals of the Mittag-Leffler function and the piecewise polynomial interpolation method. Two methods have been developed to approximate the Mittag-Leffler function based on the Taylor series and the Wright function. The proposed time discretization is capable of achieving (1+α)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(1+\alpha )$$\end{document}th order convergence, where the fractional order α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} ranges from 0 to 1. Numerical experiments are presented to verify our theoretical results.
NETL
NSTL
Springer Nature
