Numerical Method for the Deterministic Kardar-Parisi-Zhang Equation in Unbounded Domains

Abstract

We propose an artificial boundary method for solving the deterministic Kardar-Parisi-Zhang equation in one-, two- and three- dimensional unbounded domains. The exact artificial boundary conditions are obtained on the artificial boundaries. Then the original problems are reduced to equivalent problems in bounded domains. A finite difference method is applied to solve the reduced problems, and some numerical examples are provided to show the effectiveness of the method.