A fractional Tikhonov method for solving a Cauchy problem of Helmholtz equation |
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Authors: | Zhi Qian Xiaoli Feng |
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Institution: | 1. Department of Mathematics, Nanjing University, Nanjing, China.zqian@nju.edu.cn;3. School of Mathematics and Statistics, Xidian University, Xi’an, China. |
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Abstract: | In this paper, we study a fractional Tikhonov regularization method (FTRM) for solving a Cauchy problem of Helmholtz equation in the frequency domain. On the one hand, the FTRM retains the advantage of classical Tikhonov method. On the other hand, our method can prevent the effect of oversmoothing of classical Tikhonov method and conveniently control the amount of damping. The convergence error estimates between the exact solution and its regularization approximation are constructed. Several interesting numerical examples are provided, which validate the effectiveness of the proposed method. |
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Keywords: | Inverse problem ill-posed problem filtering idea fractional Tikhonov method Cauchy problem for Helmholtz equation |
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