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

Abstract

We propose an artificial boundary method for solving the deterministic\r Kardar-Parisi-Zhang equation in one-, two- and three- dimensional unbounded domains.\r The exact artificial boundary conditions are obtained on the artificial boundaries. Then\r 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\r examples are provided to show the effectiveness of the method.