文章基本信息

标题：Solving the Riesz–Feller space-fractional backward diffusion problem by a generalized Tikhonov method
本地全文：下载
作者：Hongwu Zhang ; Xiaoju Zhang
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2020
卷号：2020
期号：1
页码：1-16
DOI：10.1186/s13662-020-02719-5
出版社：Hindawi Publishing Corporation
摘要：The article investigates a Riesz–Feller space-fractional backward diffusion problem. We develop a generalized Tikhonov regularization method to overcome the ill-posedness of this problem, and then based on the result of conditional stability, we derive the convergence estimates of logarithmic and double logarithmic types for the regularized method by adopting a-posteriori choice rules of regularization parameter. Finally, by using the finite difference method, we solve a direct problem to construct the data, and some corresponding results of numerical simulations are presented to verify the convergence and stability for this method.
关键词：Ill-posed problem;Riesz–Feller space-fractional backward diffusion problem;Regularization method;A-posteriori convergence estimate;Numerical simulation;