Documents published in Scipedia

• Stability in the Sense of Hyers-Ulam of Proportional Fractional Stochastic Integral Equations

  O. Alqasem, R. Fakhfakh

  
  

  Abstract

  This work investigates the existence, uniqueness, and stability in the sense of Hyers-Ulam for a class of proportional fractional Itô-Doob stochastic integral equations (PFIDSIE). To establish these properties, we employ the Banach fixed point theorem (BFPT) in combination with several fundamental mathematical inequalities that provide insight into the structure of PFIDSIEs. The approach is structured to demonstrate not only the theoretical foundation of the existence and uniqueness of solutions but also the stability of these solutions in the Hyers-Ulam sense, which ensures that approximate solutions remain close to the exact solution under small perturbations. The results contribute to the broader field of fractional stochastic differential equations, particularly in situations where fractional dynamics and stochastic processes intersect. Furthermore, the findings are illustrated through three examples, showcasing the applicability and utility of the developed theory in practical settings.OPEN ACCESS Received: 29/01/2025 Accepted: 14/03/2025 Published: 20/04/2025

  Abstract
  This work investigates the existence, uniqueness, and stability in the sense of Hyers-Ulam for a class of proportional fractional Itô-Doob stochastic integral equations [...]

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• Optimal Control Strategies for COVID-19 Epidemic Management: A Mathematical Modeling Approach Using the SEIQR Framework

  R. Ramalingam, A. Gnanaprakasam, S. Boulaaras

  
  

  Abstract

  The COVID-19 pandemic has necessitated the development of robust mathematical models to understand and mitigate its impact. This study presents a compartmental model for the Indian pandemic COVID-19 dynamics, incorporating key compartments such as susceptible, exposed, infected, quarantined, and recovered populations. The positivity and boundedness of solutions are rigorously analyzed to ensure that the model remains biologically meaningful over time. A detailed exploration of the basic reproduction number R

  Abstract
  The COVID-19 pandemic has necessitated the development of robust mathematical models to understand and mitigate its impact. This study presents a compartmental model for the [...]

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• Matrix Algorithms Based on Jacobi and Romanovski-Jacobi Polynomials for Solving the FitzHugh-Nagumo Nonlinear Equation

  R. hafez, S. Boulaaras, H. Khalifa

  
  

  Abstract

  The present paper develops and makes efficient, a new, state-of-theart numerical technique for solving the FitzHugh-Nagumo Nonlinear Equation (FH-NNE) with initial and boundary conditions, which represents perhaps the simplest mathematical model for discussing biological systems, including nerve signals and cardiac behavior. Which consists of operational matrices and spectral techniques based on Jacobi and Romanovski-Jacobi polynomials. It is ensured that the nonlinear system is modeled so accurately that it can be effectively solved to ensure the best accuracy combined with computational economy. Comparing the results with the respective numerical results, it is seen that the proposed techniques outdo the standard ones as respects accuracy and efficiency of computation.OPEN ACCESS Received: 11/01/2025 Accepted: 25/02/2025 Published: 07/04/2025

  Abstract
  The present paper develops and makes efficient, a new, state-of-theart numerical technique for solving the FitzHugh-Nagumo Nonlinear Equation (FH-NNE) with initial and boundary [...]

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• Numerical Study of a Vertical Axis Wind Turbine with an Inner Cylindrical Deflector

  N. Al-Khawlani, A. Fazlizan, A. Abdalkarem, A. Ibrahim, Z. Harun

  Rev. int. métodos numér. cálc. diseño ing. (2025). Vol. 41, (2), 25

  
  

  Abstract

  Climate change demands innovative renewable energy solutions, with wind energy emerging as a key resource. Vertical-axis wind turbines (VAWTs) are particularly suited for low-speed, turbulent wind environments due to their ability to capture wind from all directions. However, VAWTs face aerodynamic difficulties, especially at the downwind, where problems like negative torque and decreased efficiency are frequent. This study explores a novel solution for enhancing VAWT performance by incorporating an inner cylindrical deflector aimed at optimizing airflow around the blades. Using computational fluid dynamics (CFD) simulations, the study focuses on a three-bladed H-type VAWT with an airfoil profile of NACA0018 at a turbine diameter of 1 m. The simulations begin by evaluating a bare turbine arrangement, which shows negative torque beginning at an azimuth angle of about 165 degrees onwards. When a cylindrical deflector of different diameters is introduced, the torque coefficient and overall performance are greatly enhanced by a 0.3-meter diameter. The cylindrical deflector’s effectiveness is demonstrated by the 15% increase in power coefficient C pthat results from its inclusion. These results highlight how an inner cylindrical deflector could be a useful addition to VAWTs, resolving significant inefficiencies while preserving a positive angle of attack. This strategy offers a way forward for more effective VAWT designs in renewable energy systems in addition to increasing energy output. To enhance the efficiency of vertical-axis wind turbines (VAWTs) for both urban and rural applications, future research could investigate different configurations and empirically confirm these findings.OPEN ACCESS Received: 21/01/2025 Accepted: 10/03/2025 Published: 20/04/2025

  Abstract
  Climate change demands innovative renewable energy solutions, with wind energy emerging as a key resource. Vertical-axis wind turbines (VAWTs) are particularly suited for [...]

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• A Fully Coupled Mechano-Chemical Digital Model for Environment-Induced Damage and Damage Propagation

  S. Lv, W. He, Y. Miao, W. Zhang, T. Srivatsan

  Rev. int. métodos numér. cálc. diseño ing. (2025). Vol. 41, (2), 24

  
  

  Abstract

  It is vital to enable and establish both comprehension and simulation of environment-induced damage processes for predicting the remaining service life of engineering structures and components, conducting reliability analysis, and designing to enhance the material’s overall resistance to such damage. A fully coupled mechano-chemical peridynamic (PD) model for environment-induced degradation, including corrosion, was developed based on both peridynamic corrosion theory and the mechano-chemical effect theory. When the conditions for phase transition are satisfied, the movement of boundaries occurs autonomously, without requiring any supplementary boundary conditions to be specified within the model. This model effectively simulates degradation arising from the combined and interactive influences of mechano-chemical phenomena. To validate the model, in-situ electrochemical tests and stress corrosion cracking tests were conducted, with the results used to explore the effects of stress and/or load on the kinetics of environment-induced damage in an aluminum alloy. The experimental electrochemical parameter values closely match theoretical predictions, validating the mechano-chemical effects. As stress levels increase, the corrosion potential of aluminum alloy 7050 shifts negatively, corrosion current density increases, and the severity of corrosion worsens. The explicit finite difference method was employed to simulate the damage evolution of a typical stress corrosion crack in the aluminum alloy. This numerical model easily simulates the morphological evolution of corrosion pits with arbitrary shapes under different stress conditions during growth. The numerical predictions closely match the experimental findings. This innovative study demonstrates that the fully coupled mechano-chemical peridynamic corrosion model can accurately capture environment-induced damage and is a valuable tool for investigating the propagation and growth of such damage in aggressive environments.OPEN ACCESS Received: 24/07/2024 Accepted: 15/11/2024 Published: 20/04/2025

  Abstract
  It is vital to enable and establish both comprehension and simulation of environment-induced damage processes for predicting the remaining service life of engineering structures [...]

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• Coupled Magnetothermal Effects in Biomagnetic Fluid Flow over a Stretched Sheet with Copper Nanoparticles

  H. Zuberi, N. Zainal

  Rev. int. métodos numér. cálc. diseño ing. (2025). Vol. 41, (2), 23

  
  

  Abstract

  The study of biomagnetic nanofluids has gained significant attention due to their applications in biomedical engineering and thermal management systems, where precise control of heat and fluid flow is crucial. This research investigates the coupled effects of a magnetic dipole, thermal radiation, and copper nanoparticles on biomagnetic nanofluid flow over a stretching sheet to analyze their impact on velocity and temperature distribution. The governing equations are solved numerically using MATLAB’s bvp4c solver over the computational domain [0, 20], and results are validated against benchmark studies to ensure accuracy. Findings reveal that increasing nanoparticle volume fraction enhances thermal conductivity but reduces velocity due to increased viscosity, while stronger ferromagnetic interactions intensify localized heating, significantly altering temperature gradients. Additionally, streamline analysis illustrates the magnetic field’s influence on flow structures, and surface plots provide a comprehensive visualization of heat dissipation within the nanofluid. The study also highlights the role of viscous dissipation and Prandtl number in thermal regulation, offering insights applicable to magnetic hyperthermia treatments, targeted drug delivery, and advanced cooling technologies.OPEN ACCESS Received: 18/02/2025 Accepted: 21/03/2025 Published: 20/04/2025

  Abstract
  The study of biomagnetic nanofluids has gained significant attention due to their applications in biomedical engineering and thermal management systems, where precise control [...]

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• A Sphalt Crack Recognition Algorithm Based on Fuzzy Automatic Threshold C-Means Clustering Algorithm

  G. Zheng, Z. Jiang

  Rev. int. métodos numér. cálc. diseño ing. (2025). Vol. 41, (2), 22

  
  

  Abstract

  Cracks are the most significant type of pavement disease, and the precise segmentation of cracks serves as an important decision-making basis for national preventive road maintenance management. In response to the problem of crack segmentation accuracy of existing pavement models under complex backgrounds, a crack recognition algorithm for remote sensing images based on the Fuzzy Automatic Threshold C-Means Clustering Algorithm (FATCM) was designed by incorporating local spatial and gray-level information constraints. The FATCM method can strengthen the inherent effectiveness of the traditional fuzzy C-means (FCM) algorithm, achieve uniform segmentation through fuzzy membership calculation and iterative process, and effectively eliminate edge ambiguity. The core innovation of FATCM resides in the introduction of the fuzzy local similarity measure, which is predicated upon the pixel spatial attraction model. This novel measure is astutely applied to automatically strike a refined equilibrium. Specifically, it ensures a high degree of insensitivity to noise, a factor of paramount importance in safeguarding the integrity of image data. Simultaneously, it minimizes the manifestation of edge-blurring artifacts, thereby proficiently retaining the minute and crucial details of the image. Multiple types of images in the Crack500 dataset were used in the experiments to evaluate the performance of FATCM. The experimental results show that this method has good detection results and can effectively extract weakly contrasted cracks and small cracks.OPEN ACCESS Received: 24/07/2024 Accepted: 16/12/2024 Published: 20/04/2025

  Abstract
  Cracks are the most significant type of pavement disease, and the precise segmentation of cracks serves as an important decision-making basis for national preventive road [...]

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• A Numerical Study on MHD 3-D Casson-Nanofluid Flow Past an Exponentially Stretching Sheet with Double Cattaneo-Christov Diffusion Effects

  M. Gundagani, V. Javvaji, D. Gadipalli, S. Pallerla, Q. Al-Mdallal, S. Bhati

  Rev. int. métodos numér. cálc. diseño ing. (2025). Vol. 41, (2), 21

  
  

  Abstract

  A numerical study of a three-dimensional steady-state flow of a viscous incompressible Casson fluid containing nanofluid particles interacting with a stretching sheet is the primary focus of this work. The equations for concentration and energy include the Cattaneo-Christov double diffusion effects. This work transforms deriving the controlling boundary layer equations into similarity equations using non-linear similarity transformations in three-dimensional analyses. To evaluate this study, the following was done. In the case of the combined Runge-Kutta method and the shooting approach, it is possible to provide an analytical solution for the obtained equations. Moreover, a comparative analysis of the collected data with previously published results under certain circumstances demonstrates a significant concordance between the two sets of findings. The problem is governed by thirteen physical parameters. Figures and tables are used to depict the effects of different characteristics in the following chapters, including temperature, velocity, and concentration profiles, on distinct flow distributions.OPEN ACCESS Received: 08/01/2025 Accepted: 28/03/2025 Published: 20/04/2025

  Abstract
  A numerical study of a three-dimensional steady-state flow of a viscous incompressible Casson fluid containing nanofluid particles interacting with a stretching sheet is the [...]

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• A Human-Computer Collaborative Behavior Measurement Model for Assembly in Constrained Visibility Environments

  H. Zhan, Z. Wang, Y. Wang, Q. Lu, M. Zhu

  Rev. int. métodos numér. cálc. diseño ing. (2025). Vol. 41, (2), 20

  
  

  Abstract

  Collision interference detection is an important concern in the manual installation of cable harnesses. Due to the complex and variable layout of cable harness installations, hand assembly movements are prone to collisions, contact, and other forms of interaction with surrounding equipment. Furthermore, cable harnesses often need to be routed along specific paths in visually constrained environments. Currently, there is a lack of modeling in the extraction of hand motion parameters and the data analysis of hand action intent. To address this challenge, we propose a novel human-machine collaboration behavior measurement model. This model not only provides a rapid solution for extracting hand motion parameters but also delivers efficient and natural visual feedback for the behavioral intent reflected by hand motion features. First, we introduce a hand motion parameter extraction mechanism based on a hand kinematics model. Second, we develop a virtual-to-real spatial registration model specifically designed for visually constrained conditions, enabling accurate recognition and 3D calibration of hand action intent. A user study experiment demonstrates that the proposed model outperforms traditional hand behavior measurement models in terms of manual task efficiency, hand motion recognition accuracy, and the naturalness of hand interactions. This improvement is particularly evident in visually constrained environments, effectively addressing challenges in obstacle avoidance and intent inference during spatially constrained assembly tasks.OPEN ACCESS Received: 10/09/2024 Accepted: 08/11/2024 Published: 20/04/2025

  Abstract
  Collision interference detection is an important concern in the manual installation of cable harnesses. Due to the complex and variable layout of cable harness installations, [...]

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• Stability in the Sense of Hyers-Ulam of Proportional Fractional Stochastic Integral Equations

  O. Alqasem, R. Fakhfakh

  Rev. int. métodos numér. cálc. diseño ing. (2025). Vol. 41, (2), 19

  
  

  Abstract

  This work investigates the existence, uniqueness, and stability in the sense of Hyers-Ulam for a class of proportional fractional Itô-Doob stochastic integral equations (PFIDSIE). To establish these properties, we employ the Banach fixed point theorem (BFPT) in combination with several fundamental mathematical inequalities that provide insight into the structure of PFIDSIEs. The approach is structured to demonstrate not only the theoretical foundation of the existence and uniqueness of solutions but also the stability of these solutions in the Hyers-Ulam sense, which ensures that approximate solutions remain close to the exact solution under small perturbations. The results contribute to the broader field of fractional stochastic differential equations, particularly in situations where fractional dynamics and stochastic processes intersect. Furthermore, the findings are illustrated through three examples, showcasing the applicability and utility of the developed theory in practical settings.OPEN ACCESS Received: 29/01/2025 Accepted: 14/03/2025 Published: 20/04/2025

  Abstract
  This work investigates the existence, uniqueness, and stability in the sense of Hyers-Ulam for a class of proportional fractional Itô-Doob stochastic integral equations [...]

  • 111
  •  read