A test of the boundary doubling method for the numerical solution of diffusion-reaction systems

Numerical methods for solving diffusion-influenced bimolecular reactions in the 1- and 3-dimensional Smoluchowski approach are presented. The finite-difference method is used to solve diffusion-reaction equations for the pair distribution function. The kinetic equation for the concentration is evolved by the Runge–Kutta method with an adaptive time step. The boundary doubling method is introduced to study long-time dynamics where the truncation problem of the infinite boundary is crucial. The results show remarkable accuracy and speed with small number of spatial grid points until long times.