Numerical method for restoring the initial condition for the wave equation
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 varia...
| Published in: | Вестник Томского государственного университета. Математика и механика № 88. С. 5-13 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
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| Online Access: | http://vital.lib.tsu.ru/vital/access/manager/Repository/koha:001143249 Перейти в каталог НБ ТГУ |
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| 008 | 240904|2024 ru s a eng d | ||
| 024 | 7 | |a 10.17223/19988621/88/1 |2 doi | |
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| 040 | |a RU-ToGU |b rus |c RU-ToGU | ||
| 100 | 1 | |a Gamzaev, Khanlar M. |9 969729 | |
| 245 | 1 | 0 | |a Numerical method for restoring the initial condition for the wave equation |c K. M. Gamzaev |
| 246 | 1 | 1 | |a Численный метод восстановления начального условия для волнового уравнения |
| 336 | |a Текст | ||
| 337 | |a электронный | ||
| 504 | |a Библиогр.: 18 назв. | ||
| 520 | 3 | |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. | |
| 653 | |a восстановление начального условия | ||
| 653 | |a волновые уравнения | ||
| 653 | |a обратные задачи | ||
| 653 | |a дифференциально-разностные задачи | ||
| 655 | 4 | |a статьи в журналах |9 969730 | |
| 773 | 0 | |t Вестник Томского государственного университета. Математика и механика |d 2024 |g № 88. С. 5-13 |x 1998-8621 |w 0210-41660 | |
| 852 | 4 | |a RU-ToGU | |
| 856 | 4 | |u http://vital.lib.tsu.ru/vital/access/manager/Repository/koha:001143249 | |
| 856 | |y Перейти в каталог НБ ТГУ |u https://koha.lib.tsu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=1143249 | ||
| 908 | |a статья | ||
| 999 | |c 1143249 |d 1143249 | ||
| 039 | |b 100 | ||