The Wang-Ball polynomials operational matrices of the derivatives are used in this study to solve singular perturbed second-order differential equations (SPSODEs) with boundary conditions. Using the matrix of Wang-Ball polynomials, the main singular perturbation problem is converted into linear algebraic equation systems. The coefficients of the required approximate solution are obtained from the solution of this system. The residual correction approach was also used to improve an error, and the results were compared to other reported numerical methods. Several examples are used to illustrate both the reliability and usefulness of the Wang-Ball operational matrices. The Wang Ball approach has the ability to improve the outcomes by minimizing the degree of error between approximate and exact solutions. The Wang-Ball series has shown its usefulness in solving any real-life scenario model as first- or second-order differential equations (DEs).
This paper presents on the design of L-Band Multiwavelength laser for Hybrid Time Division Multiplexing/ Wavelength Division Multiplexing (TDM/WDM) Passive Optical Network (PON) application. In this design, an L-band Mulltiwavelength Laser is designed as the downstream signals for TDM/WDM PON. The downstream signals ranging from 1569.865 nm to 1581.973 nm with 100GHz spacing. The multiwavelength laser is designed using OptiSystem software and it is integrated into a TDM/WDM PON that is also designed using OptiSystem simulation software. By adapting multiwavelength fiber laser into a TDM/WDM network, a simple and low-cost downstream signal is proposed. From the simulation design, it is found that the proposed design is suitable to be used
... Show MoreThe efficient exploitation of production inventory systems is of significant importance in the modern industrial reality. This paper explores the effect of such a system on dynamic behaviour of a system when the control is provided synergistically by a method called synergetic control (SC). The mathematical model of the system is first constructed and SC introduced to improve the responsiveness of the system when the time-varying demand condition is taken into account. To cope with the problem of unavailability of the systems' state signals and to estimate the demand, the extended state observer (ESO) is introduced. Moreover, mountain gazelle optimizer (MGO) is employed to tune the adjustable design parameters of the SC and the ESO based on
... Show MoreIn this paper, double Sumudu and double Elzaki transforms methods are used to compute the numerical solutions for some types of fractional order partial differential equations with constant coefficients and explaining the efficiently of the method by illustrating some numerical examples that are computed by using Mathcad 15.and graphic in Matlab R2015a.
In this article four samples of HgBa2Ca2Cu2.4Ag0.6O8+δ were prepared and irradiated with different doses of gamma radiation 6, 8 and 10 Mrad. The effects of gamma irradiation on structure of HgBa2Ca2Cu2.4Ag0.6O8+δ samples were characterized using X-ray diffraction. It was concluded that there effect on structure by gamma irradiation. Scherrer, crystallization, and Williamson equations were applied based on the X-ray diffraction diagram and for all gamma doses, to calculate crystal size, strain, and degree of crystallinity. I
... Show MoreJoint dysfunction disables are impacting millions of individuals worldwide. It significantly interferes with essential daily tasks like eating, drinking, and writing, often making self-care challenging for those affected. Exoskeleton robots are developed to enable individuals with impaired physical functions to perform daily activities and maintain independence. This study introduces a wearable exoskeleton control system for the elbow joint designed, providing an alternative assistive solution to traditional treatment methods. The elbow exoskeleton system used for therapy has nonlinearity and time-dependent parameters. To address these challenges, this work presents a sliding mode control (SMC) for tracking the path of an EES. To reduce the
... Show MoreSteady natural and mixed convection flow in a square vented enclosure filled with water-saturated aluminum metal foam is numerically investigated. The left vertical wall is kept at constant temperature and the remaining walls are thermally insulated. Forced convection is imposed by providing an inlet at cavity bottom surface, and a vent at the top surface. Natural convection takes place due to the temperature difference inside the enclosure. Darcy-Brinkman-Forchheimer model for fluid flow and the two-equation of the local thermal non-equilibrium model for heat flow was adopted to describe the flow characteristics within the porous cavity. Numerical results are obtained for a wide range of width of the inlet as a fraction
... Show MoreIn this paper, we introduce three robust fuzzy estimators of a location parameter based on Buckley’s approach, in the presence of outliers. These estimates were compared using the variance of fuzzy numbers criterion, all these estimates were best of Buckley’s estimate. of these, the fuzzy median was the best in the case of small and medium sample size, and in large sample size, the fuzzy trimmed mean was the best.
In this paper, a new technique is offered for solving three types of linear integral equations of the 2nd kind including Volterra-Fredholm integral equations (LVFIE) (as a general case), Volterra integral equations (LVIE) and Fredholm integral equations (LFIE) (as special cases). The new technique depends on approximating the solution to a polynomial of degree and therefore reducing the problem to a linear programming problem(LPP), which will be solved to find the approximate solution of LVFIE. Moreover, quadrature methods including trapezoidal rule (TR), Simpson 1/3 rule (SR), Boole rule (BR), and Romberg integration formula (RI) are used to approximate the integrals that exist in LVFIE. Also, a comparison between those
... Show MoreThe Korteweg-de Vries equation plays an important role in fluid physics and applied mathematics. This equation is a fundamental within study of shallow water waves. Since these equations arise in many applications and physical phenomena, it is officially showed that this equation has solitary waves as solutions, The Korteweg-de Vries equation is utilized to characterize a long waves travelling in channels. The goal of this paper is to construct the new effective frequent relation to resolve these problems where the semi analytic iterative technique presents new enforcement to solve Korteweg-de Vries equations. The distinctive feature of this method is, it can be utilized to get approximate solutions for travelling waves of
... Show MoreAbstract-Servo motors are important parts of industry automation due to their several advantages such as cost and energy efficiency, simple design, and flexibility. However, the position control of the servo motor is a difficult task because of different factors of external disturbances, nonlinearities, and uncertainties. To tackle these challenges, an adaptive integral sliding mode control (AISMC) is proposed, in which a novel bidirectional adaptive law is constructed to reduce the control chattering. The proposed control has three steps to be designed. Firstly, a full-order integral sliding manifold is designed to improve the servo motor position tracking performance, in which the reaching phase is eliminated to achieve the invariance of
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