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:: Volume 7, Issue 2 (Vol.7, No. 2, Summer 2021) ::
mr 2021, 7(2): 371-388 Back to browse issues page
Shannon Wavelet Regularization Method for the Cauchy Problem Associated with the Helmholtz Equation
Milad Karimi1, Fridoun Moradlou 2, Mojtaba Hajipour1
1- Department of Mathematics, Sahand University of Technology
2- Department of Mathematics, Sahand University of Technology , fridoun.moradlou@gmail.com
Abstract:   (183 Views)
This manuscript deals with a Shannon wavelet regularization method to solve the inverse Cauchy problem associated with the Helmholtz equation which uses to identify the radiation wave of an infinite “strip” domain. In view of Hadamard, the proposed problem extremely suffers from an intrinsic ill-posedness, i.e., the exact solution of this problem is computationally impossible to measure since any measurement or numerical computation is polluted by inevitable errors. To retrieve the solution, a regularization scheme based on Shannon wavelet is developed. The regularized solution is restored by Shannon wavelet projection on elements of Shannon multiresolution analysis. Furthermore, the concepts of convergence rate and stability of the proposed scheme are investigated and some new optimal stable estimates of the so-called Holder-Logarithmic type are rigorously derived by imposing an a priori information controlled by Sobolev scale.  The computational performance of the proposed method effectively confirms the applicability and validity of our qualitative analysis../files/site1/files/72/15Abstract.pdf
Keywords: Cauchy problem, Helmholtz equation, Shannon wavelet, Regularization
Full-Text [PDF 1067 kb]   (39 Downloads)    
Type of Study: Original Manuscript | Subject: alg
Received: 2019/02/5 | Accepted: 2019/09/25 | Published: 2021/09/1 | ePublished: 2021/09/1
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Karimi M, Moradlou F, Hajipour M. Shannon Wavelet Regularization Method for the Cauchy Problem Associated with the Helmholtz Equation. mr. 2021; 7 (2) :371-388
URL: http://mmr.khu.ac.ir/article-1-2908-en.html


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Volume 7, Issue 2 (Vol.7, No. 2, Summer 2021) Back to browse issues page
پژوهش‌های ریاضی Mathematical Researches
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