Stability estimate and the modified regularization method for a Cauchy problem of the fractional diffusion equation

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:272

Article

Xiong, Xiangtuan¹  Zhao, Liping¹  Hon, Y. C.² 

[1] Northwest Normal Univ, Dept Math, Lanzhou, Gansu, Peoples R China

[2] City Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China

关键词: Fractional diffusion equation;    III-posedness;    Stability estimate;    Regularization;    Error estimate;   

DOI  :  10.1016/j.cam.2014.05.016

来源: Elsevier

【 摘 要 】

In this paper we investigate a non-characteristic Cauchy problem for a fractional diffusion equation. Using the Fourier transformation technique, we give a conditional stability estimate on the solution. Since the problem is highly ill-posed in the Hadamard sense, a modified version of the Tikhonov regularization technique is devised for stable numerical reconstruction of the solution. An error bound with optimal order is proven. For illustration, several numerical experiments are constructed to demonstrate the feasibility and efficiency of the proposed method. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

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