On The Numerical Solution of the Nonlinear Stochastic Kadar-Parisi-Zhang Equation with Reduced Differential Transform Method

Abstract

The Reduced Differential Transform Method (RDTM) was used to obtain approximate solutions to the Kadar-Parisi-Zhang equation. The Kadar-Parisi-Zhang equation which is a stochastic nonlinear partial differential equation was used to investigate the growth (or erosion) of interfaces by particle deposition for bounded noise for an initially sinusoidal surface. The solutions obtained through RDTM with Mathematica package was compared to the finite difference solutions. The study shows the efficacy of the RDTM in solving the Kadar-Parisi-Zhang equation and is therefore a wonderful tool for solving nonlinear partial differential equations of stochastic or deterministic nature.