Implementation of Lengyel-Epstein Reaction Model for Zinc Oxide (ZnO) Nanostructures by Comparing Euler and Fourth-Order Runge–Kutta (RK) Methods

Abstract

The current study presents Lengyel-Epstein reaction model for the analysis of the reaction kinematics of the growth of Zinc oxide (ZnO) nanostructures using the fourth-order Runge-Kutta (RK) method. The aim is to propose an improved approximation technique for the computation of the concentrations of Zinc ion and Hydroxyl ion. For this purpose, a comparison of Euler's method with the fourth-order RK method was made to gauge their effectiveness in determining the concentrations of both ions. It was determined that the fourth-order RK method gives more stable results than Euler’s method. In this regard, the comparison with Euler's method showed that the rate of convergence of the RK method is more appropriate than Euler's method. Furthermore, it was also determined that the RK method validates the experimental results for the formation of ZnO nanostructures using the aqueous chemical growth (ACG) method.