روش منظم‌سازی موجک شانون برای مسئلۀ کوشی وابسته به معادلۀ هلمهولتز

نویسندگان
دانشگاه صنعتی سهند، دانشکدۀ علوم پایه، گروه ریاضی، تبریز
چکیده
در این مقاله، مسئلۀ کوشی وابسته به معادلۀ هلمهولتز برای تعیین میدان تشعشعی در یک دامنه نواری نامتناهی بررسی شده است. این مسئله در ردۀ مسائل کلاسیک به‌شدت بد وضع قرار دارد، به این معنی که اغتشاش بسیار ناچیزی در داده کوشی منجر به یک خطای بسیار بزرگ در جواب مسئله خواهد شد. با ارائه روش منظم‌سازی موجک شانون، تقریب‌های پایدار و دقیقی بین جواب تحلیلی و تقریبی مسئله در فضای مقیاس فراهم شده است. در نهایت، کارایی و دقت آنالیز کیفی روش از طریق چند مثال محاسباتی تأیید شده است.

کلیدواژه‌ها

عنوان مقاله English

Shannon Wavelet Regularization Method for the Cauchy Problem Associated with the Helmholtz Equation

نویسندگان English

Milad Karimi
fridoun Moradlou
Mojtaba Hajipour
Department of Mathematics, Sahand University of Technology
چکیده English

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

کلیدواژه‌ها English

Cauchy problem
Helmholtz equation
Shannon wavelet
Regularization
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