The Simplified Tikhonov Regularization Method for Identifying the Unknown Source for the Modified Helmholtz Equation | Zendy

Fan Yang | Zendy; HengZhen Guo | Zendy; Xiaoxiao Li | Zendy

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The Simplified Tikhonov Regularization Method for Identifying the Unknown Source for the Modified Helmholtz Equation

Author(s) -

Fan Yang,

HengZhen Guo,

Xiaoxiao Li

Publication year - 2011

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2011/953492

Subject(s) - tikhonov regularization , regularization (linguistics) , helmholtz equation , backus–gilbert method , mathematics , regularization perspectives on support vector machines , inverse problem , mathematical analysis , mathematical optimization , computer science , boundary value problem , artificial intelligence

This paper discusses the problem of determining an unknown source which depends only on one variable for the modified Helmholtz equation. This problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the data. The regularization solution is obtained by the simplified Tikhonov regularization method. Convergence estimate is presented between the exact solution and the regularization solution. Moreover, numerical results are presented to illustrate the accuracy and efficiency of this method

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