Conclusion of discrete analog for the inverse problem of acoustics
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Keywords:
the inverse problem, a problem of acoustics, Dalamber's formula, Landveber's iteration, discrete analog, a gradient, the interfaced problemAbstract
In this article approach at the numerical solution of the return problem of acoustics is considered by method of iterations of Landveber. The offered [1, 2] second approach, consists in the following: it is necessary for search of unknown coefficient from statement of a direct problem to pass to a problem which we will realize on the computer. For this purpose we write out functionality nonviscous, we will receive statement of the interfaced problem. Further by means of solutions of the direct interfaced problem we will receive a functionality gradient nonviscous after that it is possible to solve a minimization problem. This approach at the numerical solution of the return problem is more preferable as, first, equality optional has to be carried out , secondly, expression cannot be a functionality gradient nonviscous of Ф[р]. On the other hand at realization of this approach bulky calculations that pays off the best convergence are received. Thus, this approach has "pluses" and "minuses".References
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6. Nurseitova A.T., Tyulepberdinova G. A. Skhodimost of a method of iterations of Landveber for the solution of a problem of determination of acoustic rigidity // The Messenger of KAZNPU of Abay. Almaty - 2008. – Vol. 21, No. 1. – P. 215-217. – Physical and Mathematical Sciences series.
7. Tyulepberdinova G. A., Аdilzhanova S. A. Return problem of acoustics and its conditional correctness // International Journal of Mathematics and Physics, Almaty, Kazakhstan – 2014. – Vol.2, No 5. – P.7-13.
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Tyulepberdinova, G. A., Adilzhanova, S. A., & Gaziz, G. G. (2015). Conclusion of discrete analog for the inverse problem of acoustics. International Journal of Mathematics and Physics, 6(2), 56–60. Retrieved from https://ijmph.kaznu.kz/index.php/kaznu/article/view/149
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Informatics and Mathematical Modeling
