Affiliation of Author(s):数学学院

Journal:Mathematical Methods in the Applied Sciences

Key Words:Legendre spectral method; parameter estimation; stability and convergence; time-fractional DPL model; weighted and shifted Grunwald approximation

Abstract:In the current paper, a heat transfer model is suggested based on a time-fractional dual-phase-lag (DPL) model. We discuss the model in two parts, the direct problem and the inverse problem. Firstly, for solving it, the finite difference/Legendre spectral method is constructed. In the temporal direction, we employ the weighted and shifted Grunwald approximation, which can achieve second order convergence. In the spatial direction, the Legendre spectral method is used, it can obtain spectral accuracy. The stability and convergence are theoretically analyzed. For the inverse problem, the Bayesian method is used to construct an algorithm to estimate the four parameters for the model, namely, the time-fractional order alpha, the time-fractional order beta, the delay time tau(T), and the relaxation time tau(q). Next, numerical experiments are provided to demonstrate the effectiveness of our scheme, with the values of tau(q) and tau(T) for processed meat employed. We also make a comparison with another method. The data obtained for the direct problem are used in the parameter estimation. The paper provides an accurate and efficient numerical method for the time-fractional DPL model.

All the Authors:张慧

First Author:郑如梦

Indexed by:Unit Twenty Basic Research

Correspondence Author:蒋晓芸

Discipline:Natural Science

First-Level Discipline:Mathematics

Volume:43

Issue:5

Page Number:2216-2232

Translation or Not:no

Date of Publication:2020-03-01

Included Journals:SCI