Convergence of a reflection method for diffusion-controlled reactions on static sinks

The well-known method of reflections widely employed to the solution of the steady-state diffusion equation in a three-dimensional unbounded domain outside N static spherical sinks is considered. We established simple necessary and sufficient conditions for convergence of the reflection method. As a corollary the corresponding necessary and sufficient conditions for the reflection method convergence were found in case of monopole approximation. Obtained results were also applied for calculation of the region of validity of the reflection method for clusters of equal ideal sinks forming linear chain, square and simple cubic arrays in three-dimensional space.