An improved scheme for a Robin boundary condition in discrete-time random walk algorithms

Random Walk (RW) is a common numerical tool for modeling the Advection-Diffusion equation. In this work, we develop an improved scheme for incorporating a heterogeneous reaction (i.e., a Robin boundary condition) in a discrete-time RW model. In addition, we apply the approach in two test cases. We compare the improved scheme with the classical as well as with analytical and other numerical solution. We show that the new scheme can reduce the computational error significantly, relative to the first order scheme. This reduction comes at no additional computational cost.