Comparison of Adams-Bashforth-Moulton and Dormand-Prince Methods in Lengyel-Epstein Reaction Model Forming Zinc Oxide Nanostructures

This study adopts a numerical approach in the Lengyel-Epstein reaction model for forming zinc oxide (ZnO) nanostructures. It aims to determine the optimal approximation technique to analyze the growth of ion concentrations in ZnO nanostructures. For this purpose, ordinary differential equations are developed using the Dormand-Prince method in the Lengyel-Epstein reaction model. The results obtained from this technique are compared with the results obtained from the Adams-Bashforth-Moulton (ABM) method. After a comparative analysis of both methods, the results showed that the ABM method performs better than the Dormand-Prince method. The accuracy and stability of the ABM method are higher than those of the Dormand-Prince method. Furthermore, error analysis for both methods confirms that the results obtained from the former are more optimized. Moreover, this method also validates the results obtained from the experimental procedure by using the aqueous chemical growth (ACG) method to form the nanostructures of ZnO.