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All Journal International Journal of Robotics and Control Systems
Anakira, Nidal
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Control & Systems Engineering Electrical & Electronics Engineering

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Journal : International Journal of Robotics and Control Systems

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Euler-Maclaurin Method for Approximating Solutions of Initial Value Problems Alomari, Mohammad W.; Batiha, Iqbal M.; Alkasasbeh, Wala’a Ahmad; Anakira, Nidal; Jebril, Iqbal H.; Momani, Shaher
International Journal of Robotics and Control Systems Vol 5, No 1 (2025)
Publisher : Association for Scientific Computing Electronics and Engineering (ASCEE)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31763/ijrcs.v5i1.1560

Abstract

This work is dedicated to advancing the approximation of initial value problems through the introduction of an innovative and superior method inspired by the Euler-Maclaurin formula. This results in a higher-order implicit corrected method that outperforms Taylor’s and Runge–Katta’s methods in terms of accuracy. We derive an error bound for the Euler-Maclaurin higher-order method, showcasing its stability, convergence, and greater efficiency compared to the conventional Taylor and Runge-Katta methods. To substantiate our claims, numerical experiments are provided, highlighting the exceptional efficiency of our proposed method over the traditional well-known methods.
Stability Analysis of a Fractional-Order Lengyel–Epstein Chemical Reaction Model Bouaziz, Khelifa; Djeddi, Nadhir; Ogilat, Osama; Batiha, Iqbal M.; Anakira, Nidal; Sasa, Tala
International Journal of Robotics and Control Systems Vol 5, No 2 (2025)
Publisher : Association for Scientific Computing Electronics and Engineering (ASCEE)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31763/ijrcs.v5i2.1848

Abstract

In this paper, we stady a mathematical model based on a system of fractional-order differential equations to describe the dynamics of the Lengyel–Epstein chemical reaction, which is well known for exhibiting oscillatory behavior. The use of fractional derivatives allows in chemical processes compared to classical integer-order models. We specifically focus on analyzing the stability of the system’s positive equilibrium point by applying fractional calculus techniques. The stability conditions are derived and discussed in the context of the fractional-order parameters. To validate the theoretical findings, we perform numerical simulations using the Forward Euler method adapted for fractional-order systems. These simulations illustrate the impact of the fractional order on the system’s dynamic behavior and confirm the analytical results regarding equilibrium stability.
Co-Authors Alkasasbeh, Wala’a Ahmad Alomari, Mohammad W. Batiha, Iqbal M. Bouaziz, Khelifa Djeddi, Nadhir Jebril, Iqbal H. Momani, Shaher Ogilat, Osama Sasa, Tala