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|a 10.17223/19988621/88/1
|2 doi
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|a koha001143249
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|c RU-ToGU
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|a Gamzaev, Khanlar M.
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|a Numerical method for restoring the initial condition for the wave equation
|c K. M. Gamzaev
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|a Численный метод восстановления начального условия для волнового уравнения
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|a Текст
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|a электронный
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|a Библиогр.: 18 назв.
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|a The inverse problem of restoring the initial condition for the time derivative for the one-dimensional wave equation is considered. As an additional condition, the so-lution of the wave equation at a finite time is given. First, the discretization of the deriva-tive with respect to the spatial variable is carried out and the initial problem is reduced to a differential-difference problem with respect to functions depending on the time vari-able. To solve the resulting differential-difference problem, a special representation is proposed, with the help of which the problem splits into two independent differential-difference problems. As a result, an explicit formula is obtained for determining the ap-proximate value of the desired function for each discrete value of a spatial variable. The finite difference method is used for the numerical solution of the obtained differential-difference problems. The presented results of numerical experiments conducted for model problems demonstrate the effectiveness of the proposed computational algorithm.
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|a восстановление начального условия
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|a волновые уравнения
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|a обратные задачи
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|a дифференциально-разностные задачи
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|a статьи в журналах
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|t Вестник Томского государственного университета. Математика и механика
|d 2024
|g № 88. С. 5-13
|x 1998-8621
|w 0210-41660
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|a RU-ToGU
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|u http://vital.lib.tsu.ru/vital/access/manager/Repository/koha:001143249
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|a статья
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