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All Journal Journal of Robotics and Control (JRC) International Journal of Robotics and Control Systems
Momani, Shaher
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Aerospace Engineering Computer Science & IT Control & Systems Engineering Electrical & Electronics Engineering Mechanical Engineering

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Journal : International Journal of Robotics and Control Systems

 1 
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.
Fractional Approach to Two-Group Neutron Diffusion in Slab Reactors Batiha, Iqbal M.; Allouch, Nadia; Shqair, Mohammed; Jebril, Iqbal H.; Alkhazaleh, Shawkat; 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.v5i1.1524

Abstract

The two-energy neutron diffusion model in slab reactors characterizes neutron behavior across two energy groups: fast and thermal. Fast neutrons, generated by fission, decelerate through collisions, transitioning into thermal neutrons. This model employs diffusion equations to compute neutron flux distributions and reactor parameters, thereby optimizing reactor design and safety to ensure efficient neutron utilization and stable, sustained nuclear reactions. The primary objective of this research is to explore both analytical and numerical solutions to the two-energy neutron diffusion model in slab reactors. Specifically, we will utilize the Laplace transform method for an analytical solution of the two-energy neutron diffusion model. Subsequently, employing the Caputo differentiator, we transform the original neutron diffusion model into its fractional-order equivalents, yielding the fractional-order two-energy group neutron diffusion model in slab reactors. To address the resulting fractional-order system, we develop a novel approach aimed at reducing the 2β-order system to a β-order system, where β ∈ (0, 1]. This transformed system is then solved using the Modified Fractional Euler Method (MFEM), an advanced variation of the fractional Euler method. Finally, we present numerical simulations that validate our results and demonstrate their applicability.
Trapezoidal Scheme for the Numerical Solution of Fractional Initial Value Problems Batiha, Iqbal M.; Alsamad, Hebah F.; Jebril, Iqbal H.; Al-Khawaldeh, Hamzah O.; Kasasbeh, Wala’a A. Al; Momani, Shaher
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.v5i2.1795

Abstract

The purpose of this study is to recall the main concepts and definitions in relation to the fractional calculus. In light of this overview, we will propose a novel fractional version of the so-called Trapezoid method named by the fractional Trapezoid method. Such a method will then be used to numerically solve the analog version of the initial value problems called fractional initial value problem FIVPs. As consequences of the proposed numerical approach, several numerical examples will be illustrated to verify the efficiency of the proposed numerical approach.
Co-Authors Abdelnebi, Amira Al-Khawaldeh, Hamzah O. Alkasasbeh, Wala’a Ahmad Alkhazaleh, Shawkat Allouch, Nadia Alomari, Mohammad W. Alsamad, Hebah F. Anakira, Nidal Batiha, Iqbal Batiha, Iqbal M. Bendib, Issam Jebril, Iqbal H. Kasasbeh, Wala’a A. Al Ouannas, Adel Shqair, Mohammed