Error estimation and optimization of the functional algorithms of a random walk on a grid which are applied to solving the Dirichlet problem for the Helmholtz equation

We consider the algorithms of a “random walk on a grid” which are applied to global solution of the Dirichlet problem for the Helmholtz equation (the direct and conjugate methods). In the metric space $\mathbf{C}$ we construct some upper error bounds and obtain optimal values (in the sense of the error bound) of the parameters of the algorithms (the number of nodes and the sample size).