Quasirandom Sequences in Branching Random Walks *

We consider the Neumann boundary-value problem for a nonlinear Helmholtz equation. Using Green's formula, the problem can be converted into solving a nonlinear integral equation with a polynomial nonlinearity. This equation can be solved numerically using a Monte Carlo method based on “branching random walks” occurring on specially defined domains, with the parameters of the branching process depending on the coefficients of the integral equation. In this paper, we study the properties of this method when using quasirandom instead of pseudorandom numbers to construct the branching random walks. Theoretical estimates of the convergence rate have been investigated, and numerical experiments with a model problem were also performed.

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