Direct numerical method for an inverse problem of a parabolic partial differential equation

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:232

Article

Liao, Wenyuan¹  Dehghan, Mehdi²  Mohebbi, Akbar² 

[1] Univ Calgary, Dept Math & Stat, Calgary, AB T2N 1N4, Canada

[2] Amir Kabir Univ Technol, Fac Math & Comp Sci, Dept Appl Math, Tehran, Iran

关键词: High-order method;    Finite difference scheme;    Coefficient determination;    Inverse problem;   

DOI  :  10.1016/j.cam.2009.06.017

来源: Elsevier

【 摘 要 】

A coefficient inverse problem of the one-dimensional parabolic equation is solved by a high-order compact finite difference method in this paper. The problem of recovering a time-dependent coefficient in a parabolic partial differential equation has attracted considerable attention recently. While many theoretical results regarding the existence and uniqueness of the solution are obtained, the development of efficient and accurate numerical methods is still far from satisfactory. In this paper a fourth-order efficient numerical method is proposed to calculate the function u(x, t) and the unknown coefficient a(t) in a parabolic partial differential equation. Several numerical examples are presented to demonstrate the efficiency and accuracy of the numerical method. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

Free