Comparative Evaluation of Dormand Prince and Cash-Karp Method in Lengyel Epstein Reaction Model Forming Zinc Oxide (ZnO)  Nanostructures

Kaniz Fatima kaniz; Talat Sharafat Rehmani; Sarwat Ishaque

doi:10.32350/jarms.52.01

Kaniz Fatima kaniz Department of Humanities and Social Sciences, Bahria University, Karachi Campus, Pakistan
Talat Sharafat Rehmani Department of Computer Science and Quantitative, KASB Institute of Technology, Karachi, Pakistan
Sarwat Ishaque Department of Humanities and Social Sciences, Bahria University, Karachi Campus, Pakistan

DOI: https://doi.org/10.32350/jarms.52.01

Keywords: Ordinary Differential Equations, Lengyel Epstein reaction model, Dormand Prince Method, , Cash-Karp method

Abstract

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The current study employed two different numerical techniques to solve the Ordinary Differential Equations (ODEs) of the Lengyel Epstein reaction model. This was done for direct comparison with their results on
the production of Zinc oxide (ZnO) nanostructures using Dormand Prince and Cash-Karp methods. Furthermore, the study aimed to determine the numerical approximation that may provide an estimate for
the concentration of Zinc ion () and Hydroxyl ion (OH - ) in the growth process of a ZnO nanostructure. The current study utilized the Cash- Karp method to solve ODE used in the development of the Lengyel Epstein reaction model. Afterwards, the results obtained from this approach were compared with the Dormand Prince method to determine its efficiency. After appropriate detail analysis, it was determined that Cash-Karp yields more consistent results as compared to the Dormand Prince method. The simulation for the solution of ODEs offers a higher convergence rate when Cash-Karp method is used. The error margin of the Cash-Karp method is comparatively smaller than that of the Dormand Prince method which may also be verified by the experimental results of growth of ZnO nanostructures.

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