Mil’shtejn, G. N. Application of the numerical integration of stochastic equations to solving boundary-value problems with Neumann’s boundary conditions. (English. Russian original) Zbl 0888.60050 Theory Probab. Appl. 41, No. 1, 170-177 (1996); translation from Teor. Veroyatn. Primen. 41, No. 1, 210-218 (1996). Summary: A number of methods are presented for constructing a Markov chain with reflection such that the mathematical expectation of a certain functional of a chain path is close to the solution of the Neumann problem for parabolic equations. This Markov chain weakly approximates the solution of the system of stochastic differential equations which is characteristic for the Neumann problem. For the methods under consideration, convergence theorems are obtained with the order of accuracy with respect to approximation step. Cited in 6 Documents MSC: 60H15 Stochastic partial differential equations (aspects of stochastic analysis) 65C99 Probabilistic methods, stochastic differential equations Keywords:numerical integration of stochastic differential equations; weak approximation of solutions of stochastic differential equations; one-step order of accuracy of a method; Monte Carlo methods for solving problems of mathematical physics PDFBibTeX XMLCite \textit{G. N. Mil'shtejn}, Theory Probab. Appl. 41, No. 1, 170--177 (1996; Zbl 0888.60050); translation from Teor. Veroyatn. Primen. 41, No. 1, 210--218 (1996)