The solution to direct and inverse problems for oscillation's equation with Monte Carlo methods
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 2 (1999) no. 2, pp. 99-110.

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

There are the well-known probabilistic methods for solving the elliptic and parabolic problems of mathematical physics. As for hyperbolic equations the probabilistic methods are used very seldom. In this work the Monte Carlo algorithm for solving the inverse and direct problems of the oscillation's equation is presented.
@article{SJVM_1999_2_2_a0,
     author = {I. I. Belinskaya},
     title = {The solution to direct and inverse problems for oscillation's equation with {Monte} {Carlo} methods},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {99--110},
     publisher = {mathdoc},
     volume = {2},
     number = {2},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_1999_2_2_a0/}
}
TY  - JOUR
AU  - I. I. Belinskaya
TI  - The solution to direct and inverse problems for oscillation's equation with Monte Carlo methods
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 1999
SP  - 99
EP  - 110
VL  - 2
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJVM_1999_2_2_a0/
LA  - ru
ID  - SJVM_1999_2_2_a0
ER  - 
%0 Journal Article
%A I. I. Belinskaya
%T The solution to direct and inverse problems for oscillation's equation with Monte Carlo methods
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 1999
%P 99-110
%V 2
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJVM_1999_2_2_a0/
%G ru
%F SJVM_1999_2_2_a0
I. I. Belinskaya. The solution to direct and inverse problems for oscillation's equation with Monte Carlo methods. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 2 (1999) no. 2, pp. 99-110. http://geodesic.mathdoc.fr/item/SJVM_1999_2_2_a0/

[1] Vladimirov B. C., Uravneniya matematicheskoi fiziki, Nauka, M., 1981 | MR

[2] Ermakov S. M., Mikhailov G. A., Statisticheskoe modelirovanie, Nauka, M., 1982 | MR

[3] Kabanikhin S. I., Proektsionno-raznostnye metody opredeleniya koeffitsientov giperbolicheskikh uravnenii, Nauka, Novosibirsk, 1988 | MR | Zbl

[4] Kabanikhina I. I., “Chislennaya realizatsiya algoritma Monte-Karlo dlya obratnoi zadachi dlya matrichnogo analoga uravneniya akustiki”, Tr. VTs SO RAN. Ser. Teoriya i prilozheniya statisticheskogo modelirovaniya, Novosibirsk, 1988, 46–53

[5] Kurant R., Gilbert D., Metody matematicheskoi fiziki, v. 2, GTTI, M., L., 1965

[6] Levitan B. M., “Ob asimptoticheskom povedenii spektralnoi funktsii i razlozhenie po sobstvennym funktsiyam uravneniya $\Delta u+\lambda-q(x)u=0$”, Tr. mosk. mat. ob-va, 4, M., 1955, 67–82 | MR

[7] Mikhailov G. A., Optimizatsiya vesovykh metodov Monte-Karlo, Nauka, M., 1987 | MR

[8] Romanov V. G., Obratnye zadachi matematicheskoi fiziki, Nauka, M., 1984 | MR