The method of operational matrices based on different types of polynomials such as Bernstein, shifted Legendre and Bernoulli polynomials will be presented and implemented to solve the nonlinear Blasius equations approximately. The nonlinear differential equation will be converted into a system of nonlinear algebraic equations that can be solved using Mathematica®12. The efficiency of these methods has been studied by calculating the maximum error remainder ( ), and it was found that their efficiency increases as the polynomial degree (n) increases, since the errors decrease. Moreover, the approximate solutions obtained by the proposed methods are compared with the solution of the 4th order Runge-Kutta method (RK4), which gives very good agreement. In addition, the convergence of the proposed approximate methods is given based on one of the Banach fixed point theorem results.
Sliding Mode Controller (SMC) is a simple method and powerful technique to design a robust controller for nonlinear systems. It is an effective tool with acceptable performance. The major drawback is a classical Sliding Mode controller suffers from the chattering phenomenon which causes undesirable zigzag motion along the sliding surface. To overcome the snag of this classical approach, many methods were proposed and implemented. In this work, a Fuzzy controller was added to classical Sliding Mode controller in order to reduce the impact chattering problem. The new structure is called Sliding Mode Fuzzy controller (SMFC) which will also improve the properties and performance of the classical Sliding Mode control
... Show MoreWith the continuous downscaling of semiconductor processes, the growing power density and thermal issues in multicore processors become more and more challenging, thus reliable dynamic thermal management (DTM) is required to prevent severe challenges in system performance. The accuracy of the thermal profile, delivered to the DTM manager, plays a critical role in the efficiency and reliability of DTM, different sources of noise and variations in deep submicron (DSM) technologies severely affecting the thermal data that can lead to significant degradation of DTM performance. In this article, we propose a novel fault-tolerance scheme exploiting approximate computing to mitigate the DSM effects on DTM efficiency. Approximate computing in hardw
... Show MoreThis paper presents a newly developed method with new algorithms to find the numerical solution of nth-order state-space equations (SSE) of linear continuous-time control system by using block method. The algorithms have been written in Matlab language. The state-space equation is the modern representation to the analysis of continuous-time system. It was treated numerically to the single-input-single-output (SISO) systems as well as multiple-input-multiple-output (MIMO) systems by using fourth-order-six-steps block method. We show that it is possible to find the output values of the state-space method using block method. Comparison between the numerical and exact results has been given for some numerical examples for solving different type
... Show MoreThe purpose of this research is to implement the orthogonal polynomials associated with operational matrices to get the approximate solutions for solving two-dimensional elliptic partial differential equations (E-PDEs) with mixed boundary conditions. The orthogonal polynomials are based on the Standard polynomial (
This research aims to test the ability of glass waste powder to adsorb cadmium from aqueous solutions. The glass wastes were collected from the Glass Manufacturing Factory in Ramadi. The effect of concentration and reaction time on sorption was tested through a series of laboratory experiments. Four Cd concentrations (20, 40, 60, and 80) as each concentration was tested ten times for 5, 10, 15, 20, 25, 30, 35, 40, 45, and 50 min. Solid (glass wastes) to liquid was 2g to 30ml was fixed in each experiment where the total volume of the solution was 30ml. The pH, total dissolved salts and electrical conductivity were measured at 30ºC. The equilibrium concentration was determined at 25 minutes, thereafter it was noted that the sorption
... Show MoreAbstract
A surface fitting model is developed based on calorimeter data for two famous brands of household compressors. Correlation equations of ten coefficient polynomials were found as a function of refrigerant saturating and evaporating temperatures in range of (-35℃ to -10℃) using Matlab software for cooling capacity, power consumption, and refrigerant mass flow rate.
Additional correlations equations for these variables as a quick choice selection for a proper compressor use at ASHRAE standard that cover a range of swept volume range (2.24-11.15) cm3.
The result indicated that these surface fitting models are accurate with in ± 15% for 72 compressors model of cooling cap
... Show Moren this paper, we formulate three mathematical models using spline functions, such as linear, quadratic and cubic functions to approximate the mathematical model for incoming water to some dams. We will implement this model on dams of both rivers; dams on the Tigris are Mosul and Amara while dams on the Euphrates are Hadetha and Al-Hindya.
A huge potential from researchers was presented for enhancing the nonlinear optical response for materials that interacts by light. In this work, we study the nonlinear optical response for chemically prepared nano- fluid of silver nanoparticles in de-ionized water with TSC (Tri-sodium citrate) protecting agent. By the means of self-defocusing technique and under CW 473 nm blue laser, the reflected diffraction pattern were observed and recorded by CCD camera. The results demonstrate that, the Ag nano-fluid shows a good third order nonlinear response and the magnitude of the nonlinear refractive index was in the order of 10−7 cm2/W. We determine the maximum change of the nonlinear refractive index and the related phase shift for the mat
... Show MoreIn 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 More