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A regularization method for the cauchy problem of the modified Helmholtz equation
Author(s) -
Cheng Hao,
Zhu Ping,
Gao Jie
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3311
Subject(s) - mathematics , helmholtz equation , regularization (linguistics) , a priori and a posteriori , cauchy problem , cauchy distribution , backus–gilbert method , cauchy's convergence test , helmholtz free energy , mathematical analysis , tikhonov regularization , initial value problem , inverse problem , cauchy boundary condition , regularization perspectives on support vector machines , computer science , boundary value problem , philosophy , epistemology , artificial intelligence , free boundary problem , physics , quantum mechanics
In the present paper, an iteration regularization method for solving the Cauchy problem of the modified Helmholtz equation is proposed. The a priori and a posteriori rule for choosing regularization parameters with corresponding error estimates between the exact solution and its approximation are also given. The numerical example shows the effectiveness of this method. Copyright © 2014 John Wiley & Sons, Ltd.