Transparent Boundary Condition for the Parabolic Equation Modeled by the 4RW

Transparent boundary condition in a 2D-space is presented for the four-state random walk (4RW) model that is used in treating the standard parabolic equation by stochastic methods. The boundary condition is exact for the discrete 4RW model, is of explicit type, and relates the field in the spectral domain at the boundary point in terms of the field at a previous interior point via a spectral transfer function. In the spatial domain, the domain of influence for the boundary condition is directly proportional to the time elapsed. By performing various approximations to the transfer function, several approximate absorbing boundary conditions can be derived that have much more limited domain of influence.