References
C. Miranda, Partial Differential Equations of Elliptic Type [Russian translation], Izdat. Inostr. Lit., Moscow (1957).
S. M. Ermakov and G. A. Mikhaîlov, Statistical Modeling [in Russian], Nauka, Moscow (1982).
G. A. Mikhailov, New Monte Carlo Methods with Estimating Derivatives, VSP, Utrecht and Tokyo (1995).
M. E. Muller, “some continuous Monte Carlo methods for the Dirichlet problem” Ann. Math. Statist.,27, No. 3, 569–589 (1956).
A. A. Kronberg, “On algorithms for statistical modeling of the solution of boundary value problems of elliptic type” Zh. Vychisl. Mat. i Mat. Fiz.,24, No. 10, 1531–1537 (1984).
G. A. Mikhaîlov and A. F. Cheshkova, “Solving the difference Dirichlet problem for the Helmholtz multidimensional equation by the Monte Carlo method”, Zh. Vychisl. Mat. i Mat. Fiz. (to appear).
Additional information
The research was financially supported by the Russian Foundation for Basic Research (Grant 97-01-00855).
Novosibirsk. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 38, No. 3, pp. 603–614, May–June, 1997.
Rights and permissions
About this article
Cite this article
Mikhaĭlov, G.A., Makarov, R.N. Solution of boundary value problems of the second and third kinds by the monte carlo methods. Sib Math J 38, 518–527 (1997). https://doi.org/10.1007/BF02683840
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02683840