A new Monte Carlo method for solving a stationary diffusion equation (Q1594587)

The authors construct a special probability representation and an appropriate Monte Carlo method for solving a stationary diffusion equation in a domain \(\Omega\) with a degenerate convective part on \(\partial\Omega\). This method is important in applications, since a numerical realization of the standard probability representation in the stationary case admits sufficiently accurate estimates of a determinate error only for small domains. Moreover, the method provides asymptotically unbiased estimates of parametric derivatives and makes it possible to estimate the probability moments of solutions to the problems with random parameters. The authors show that the degenerate condition of the convective part of the diffusion operator can be omitted if one passes to the direct modeling of diffusion trajectories in a boundary layer.