Geodesic
Numerical method for restoring the initial condition for the wave equation
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 88 (2024), pp. 5-13

Voir la notice de l'article provenant de la source Math-Net.Ru

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 solution of the wave equation at a finite time is given. First, the discretization of the derivative 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 variable. 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 approximate 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.
Keywords: wave equation, inverse problem, recovery of the initial condition, differential-difference problem. 
@article{VTGU_2024_88_a0,
     author = {Kh. M. Gamzaev},
     title = {Numerical method for restoring the initial condition for the wave equation},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {5--13},
     publisher = {mathdoc},
     number = {88},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2024_88_a0/}
}
TY  - JOUR
AU  - Kh. M. Gamzaev
TI  - Numerical method for restoring the initial condition for the wave equation
JO  - Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika
PY  - 2024
SP  - 5
EP  - 13
IS  - 88
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VTGU_2024_88_a0/
LA  - en
ID  - VTGU_2024_88_a0
ER  - 
%0 Journal Article
%A Kh. M. Gamzaev
%T Numerical method for restoring the initial condition for the wave equation
%J Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika
%D 2024
%P 5-13
%N 88
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VTGU_2024_88_a0/
%G en
%F VTGU_2024_88_a0
Kh. M. Gamzaev. Numerical method for restoring the initial condition for the wave equation. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 88 (2024), pp. 5-13. http://geodesic.mathdoc.fr/item/VTGU_2024_88_a0/