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References
B. S. Elepov, A. A. Kronberg, G. A. Mikhailov, and K. K. Sabel'fel'd, Solution of Boundary Value Problems by the Monte Carlo Method [in Russian], Nauka, Novosibirsk (1980).
S. M. Ermakov, V. V. Nekrutkin, and A. S. Sipin, Stochastic Processes for Solving Classical Equations of Mathematical Physics [in Russian], Nauka, Moscow (1984).
O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural'tseva, Linear and Quasilinear Equations of Parabolic Type [in Russian], Nauka, Moscow (1967).
G. A. Mikhailov, “New Monte Carlo methods for solving the Helmholtz equation,” Dokl. RAN,326, No. 6, 943–947 (1992).
G. A. Mikhailov, “Solving the Dirichlet problem for nonlinear elliptic equations by the Monte Carlo method,” Sibirsk. Mat. Zh.,35, No. 5, 967–976 (1994).
S. M. Ermakov and G. A. Mikhailov, Statistical Modeling [in Russian], Nauka, Moscow (1982).
G. A. Mikhailov, Optimization of Weighted Monte Carlo Methods [in Russian], Nauka, Moscow (1987).
G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Darbinyan, B. A. Kargin, and B. S. Elepov, The Monte Carlo Method in Atmospheric Optics [in Russian], Nauka, Novosibirsk (1976).
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Dedicated to the jubilee of the 70th birthday of my teacher Academician G. I. Marchuk.
The research was supported by the Russian Foundation for Fundamental Research (Grant 93-01-00500) and the International Science Foundation (Grant PC 000).
Translated fromSibirskii Matematicheskii Zhurnal, Vol. 36, No. 3, pp. 602–610, May–June, 1995.
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Mikhailov, G.A. The Monte Carlo methods for solving the vector and Stochastic Helmholtz equations. Sib Math J 36, 517–525 (1995). https://doi.org/10.1007/BF02109839
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DOI: https://doi.org/10.1007/BF02109839