Exponential stability of the nonlinear transmission acoustic problem

Алиев, А. Б.; Isayeva, S. E.

doi:10.1002/mma.5215

Cited by 3 publications

(1 citation statement)

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“…As is known, most of the inverse problems of geophysics is devoted to determining the speed of sound in the framework of the wave equation or its various approximations. It is assumed that other parameters of the medium, such as the density and absorption of the medium, are constant and known (Evstigneev et al, 2016;Chkadua, 2017;Aliev and Isayeva, 2018;You et al, 2018). Knowledge of this single parameter of the medium -the speed of sound is sufficient in many practical cases.…”

Section: Introductionmentioning

confidence: 99%

Comparative Analysis of Numerical Methods of the Solution of a Onedimensional Inverse Problem of Acoustics

Tyulepberdinova¹,

Oralbekova²,

Gaziz³

et al. 2020

PTQ

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Nowadays, a large number of methods for solving inverse problems arising in electrodynamics and acoustics have been developed, but the development of practical systems is necessary to combine a large number of equations that contribute to the substantiation of numerical methods for solving various multidimensional problems. Therefore, the main goal of the work is a comparative analysis of statistical methods for solving the one-dimensional inverse acoustic problem, as well as in the search for acoustic resistance. To achieve this goal, the means of description and comparison, which contributed to the identification of the characteristics of acoustic impedance, were used. Also, the finite-difference solution method, the differential circuit circulation method, and the Landweber iteration method were used. It was established that the inversion method of the difference scheme is expedient to apply in the case when additional information is known accurately enough, and the reconstructed solution is quite smooth. It was determined that if one of these conditions is violated, the method of reversing the difference scheme becomes unstable. The problems of the correctness of the issues for the wave equation with complex velocity in the one-dimensional and spatial cases were investigated. Formulas for solving these problems were obtained – analogs of classical formulas. Numerical computations show the kind of results that may be expected from the method under consideration. The materials of the paper imply the practical significance for the university teachers of the information technology specializations.

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Section: Introductionmentioning

confidence: 99%