Parameter estimation for the time fractional heat conduction model based on experimental heat flux data

• Published in: Applied mathematics letters Vol. 102; p. 106094
• Main Authors: Chi, Xiaoqing, Yu, Bo, Jiang, Xiaoyun
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.04.2020
• Subjects: Cuckoo search algorithm; Fractional heat conduction equation; Parameter estimation; Spectral collocation method; Spectral collocation method; Fractional heat conduction equation; Parameter estimation; Cuckoo search algorithm
• ISSN: 0893-9659; 1873-5452
• DOI: 10.1016/j.aml.2019.106094

In this paper, a time fractional heat conduction model is built to describe the heat transfer process in coalbed methane adsorption. A spectral collocation scheme with time discretized by the finite difference method and space discretized by Legendre collocation method is introduced to obtain the numerical solution of the fractional model. In addition, a new optimization algorithm, called the cuckoo search (CS) algorithm, is first proposed to estimate the parameters of fractional heat conduction model with the adsorption experimental heat flux data and is proved to be effective. Sensitivity analysis of model parameters and stability analysis of the CS algorithm for the fractional model are carried out at last.