کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4637796 | 1631982 | 2017 | 23 صفحه PDF | دانلود رایگان |
In this paper, we rigorously investigate the truncation method for the Cauchy problem of Helmholtz equations which is widely used to model propagation phenomena in physical applications. The truncation method is a well-known approach to the regularization of several types of ill-posed problems, including the model postulated by Regińska and Regiński (2006). Under certain specific assumptions, we examine the ill-posedness of the non-homogeneous problem by exploring the representation of solutions based on Fourier mode. Then the so-called regularized solution is established with respect to a frequency bounded by an appropriate regularization parameter. Furthermore, we provide a short analysis of the nonlinear forcing term. The main results show the stability as well as the strong convergence confirmed by the error estimates in L2L2-norm of such regularized solutions. Besides, the regularization parameters are formulated properly. Finally, some illustrative examples are provided to corroborate our qualitative analysis.
Journal: Journal of Computational and Applied Mathematics - Volume 309, 1 January 2017, Pages 56–78