标题:A time-space spectral method for the time-space fractional Fokker–Planck equation and its inverse problem
作者:Zhang, Hui ;Jiang, Xiaoyun ;Yang, Xiu
作者机构:[Zhang, Hui ;Jiang, Xiaoyun ;Yang, Xiu ] School of Mathematics, Shandong University, Jinan; 250100, China
通讯作者:Jiang, Xiaoyun
来源:Applied Mathematics and Computation
出版年:2018
卷:320
页码:302-318
DOI:10.1016/j.amc.2017.09.040
摘要:In the paper, we consider a time-space spectral method to get the numerical solution of time-space fractional Fokker–Planck initial-boundary value problem. The temporal discretization is constructed by Jacobi polynomials and the spatial discretization is composed by Legendre polynomials. Moreover, we present the stability and convergence analysis strictly. The main advantages of the provided method are spectrally accurate in time and space and high computational efficiency. In addition, we introduce the inverse problem based on the spectral form with high-order accuracy of the direct problem for the first time, the Levenberg–Marquardt (L–M) method is proposed to estimate the two fractional derivatives α and 2β. Some numerical results presented are consistent with the theoretical analysis.
© 2017 Elsevier Inc.
收录类别:EI
资源类型:期刊论文
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