Affiliation of Author(s):数学学院

Journal:Applied Mathematics and Computation

Key Words:Caputo fractional derivative; Fractional thermal wave model; Spherical composite medium; Finite difference; Inverse problem

Abstract:In this paper, we formulate a fractional thermal wave model for a bi-layered spherical tissue. Implicit finite difference method is employed to obtain the solution of the direct problem. The inverse analysis for simultaneously estimating the Caputo fractional derivative and the relaxation time parameters is implemented by means of the LevenbergMarquardt method. Compared with the experimental data, we can obviously find out that the estimated temperature increase values are excellently consistent with the measured temperature increase values in the experiment. We have also discussed the effect of the fractional derivative, the relaxation time parameters, the initial guess as well as the sensitivity problem. All the results show that the proposed fractional thermal wave model is efficient and accurate in modeling the heat transfer in the hyperthermia experiment, and the proposed numerical method for simultaneously estimating multiple parameters for the fractional thermal wave model in a spherical composite medium is effective.

All the Authors:Wang Chu

First Author:yubo

Indexed by:Unit Twenty Basic Research

Correspondence Author:Jiang Xiaoyun

Document Code:72F26AE424204E67ABFE7F29BD717AD8

Discipline:Natural Science

First-Level Discipline:Mathematics

Volume:274

Page Number:106-118

Translation or Not:no

Date of Publication:2016-02-01

Included Journals:SCI