In this paper, a new third kind Chebyshev wavelets operational matrix of derivative is presented, then the operational matrix of derivative is applied for solving optimal control problems using, third kind Chebyshev wavelets expansions. The proposed method consists of reducing the linear system of optimal control problem into a system of algebraic equations, by expanding the state variables, as a series in terms of third kind Chebyshev wavelets with unknown coefficients. Example to illustrate the effectiveness of the method has been presented.
In this paper, three approximate methods namely the Bernoulli, the Bernstein, and the shifted Legendre polynomials operational matrices are presented to solve two important nonlinear ordinary differential equations that appeared in engineering and applied science. The Riccati and the Darcy-Brinkman-Forchheimer moment equations are solved and the approximate solutions are obtained. The methods are summarized by converting the nonlinear differential equations into a nonlinear system of algebraic equations that is solved using Mathematica®12. The efficiency of these methods was investigated by calculating the root mean square error (RMS) and the maximum error remainder (𝑀𝐸𝑅n) and it was found that the accuracy increases with increasi
... Show MoreIn this paper, the methods of weighted residuals: Collocation Method (CM), Least Squares Method (LSM) and Galerkin Method (GM) are used to solve the thin film flow (TFF) equation. The weighted residual methods were implemented to get an approximate solution to the TFF equation. The accuracy of the obtained results is checked by calculating the maximum error remainder functions (MER). Moreover, the outcomes were examined in comparison with the 4th-order Runge-Kutta method (RK4) and good agreements have been achieved. All the evaluations have been successfully implemented by using the computer system Mathematica®10.
In this paper,the homtopy perturbation method (HPM) was applied to obtain the approximate solutions of the fractional order integro-differential equations . The fractional order derivatives and fractional order integral are described in the Caputo and Riemann-Liouville sense respectively. We can easily obtain the solution from convergent the infinite series of HPM . A theorem for convergence and error estimates of the HPM for solving fractional order integro-differential equations was given. Moreover, numerical results show that our theoretical analysis are accurate and the HPM can be considered as a powerful method for solving fractional order integro-diffrential equations.
... Show MoreThis research revolves around the study of sports press coverage to the third African Youth Games that took place in Algeria from 19 to 28 July 2018. The games featured approximately 3000 athletes from 54 countries who competed in 27 sports. Five sports were qualified for the Youth Olympic Games in Argentina. The aim of this study was to analyze the content of the Algerian newspaper Ennahar El-Djadid by focusing on the discussions of various sports activities during the event. Thus, the descriptive approach and content analysis method were adopted for this research. They were used to highlight the newspaper's interest in this sports phenomenon. The chosen study samples were ten issue numbers of Ennahar El-Djadid newspaper
Abstract
In this investigation, Al2O3 nano material of 50nm particles size were added to the 6061 Al aluminium alloy by using the stir casting technique to fabricate the nanocomposite of 10wt% Al2O3. The experimental results observed that the addition of 10wt% Al2O3 improved the fatigue life and strength of constant and cumulative fatigue. Comparison between the S-N curves behaviour of metal matrix (AA6061) and the nanocomposite 10wt% Al2O3 has been made. The comparison revealed that 12.8% enhancement in fatigue strength at 107cycles due to 10wt% nano reinforcement. Also cumulative fatigue l
... Show MoreAmputation of the upper limb significantly hinders the ability of patients to perform activities of daily living. To address this challenge, this paper introduces a novel approach that combines non-invasive methods, specifically Electroencephalography (EEG) and Electromyography (EMG) signals, with advanced machine learning techniques to recognize upper limb movements. The objective is to improve the control and functionality of prosthetic upper limbs through effective pattern recognition. The proposed methodology involves the fusion of EMG and EEG signals, which are processed using time-frequency domain feature extraction techniques. This enables the classification of seven distinct hand and wrist movements. The experiments conducte
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