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Novel Approximate Solutions for Nonlinear Blasius Equations
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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.

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Publication Date
Tue Oct 01 2024
Journal Name
Journal Of Physics: Conference Series
The operational matrices for Elliptic Partial Differential Equations with mixed boundary conditions
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Abstract<p>The 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 (<italic>x<sup>i</sup> </italic>), Legendre, Chebyshev, Bernoulli, Boubaker, and Genocchi polynomials. This study focuses on constructing quick and precise analytic approximations using a simple, elegant, and potent technique based on an orthogonal polynomial representation of the solution as a double power series. Consequently, a linear </p> ... Show More
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Publication Date
Tue Mar 01 2016
Journal Name
Journal Of Engineering
Design and Simulation of Sliding Mode Fuzzy Controller for Nonlinear System
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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

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Publication Date
Mon Jan 01 2018
Journal Name
Https://medwelljournals.com/journalhome.php?jid=1816-949x
Some generalized n-tuplet coincidence point theorems for nonlinear contraction mappings
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Publication Date
Sun Jun 07 2015
Journal Name
Baghdad Science Journal
Direct method for Solving Nonlinear Variational Problems by Using Hermite Wavelets
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In this work, we first construct Hermite wavelets on the interval [0,1) with it’s product, Operational matrix of integration 2^k M×2^k M is derived, and used it for solving nonlinear Variational problems with reduced it to a system of algebric equations and aid of direct method. Finally, some examples are given to illustrate the efficiency and performance of presented method.

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Publication Date
Thu Jun 10 2010
Journal Name
Iraqi Journal Of Laser
Improvement of Nonlinear Optical Properties for Mixture Laser Dyes Doped PMMA
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The spectral characteristics and the nonlinear optical properties of the mixed donor (C-480) acceptor (Rh-6G) have been determined. The spectral characteristics are studied by recording their absorption and fluorescence spectra. The nonlinear optical properties were measured by z-scan technique, using Q-switched Nd: YAG laser with 1064 nm wavelength. The results showed that the optimum concentration of acceptor is responsible for increasing the absorption and the emission bandwidth of donor to full range and to 242 nm respectively by the energy transfer process, also the efficiency of the process was increased by increasing the donor and acceptor concentration. The obtained nonlinear properties results of the mixture C-480/ Rh-6G showed

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Publication Date
Thu Dec 31 2015
Journal Name
Al-khwarizmi Engineering Journal
Prediction of Performance Equations for Household Compressors Depending on Manufacturing Data for Refrigerators and Freezers
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Abstract

 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

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Publication Date
Thu Oct 01 2020
Journal Name
Ieee Transactions On Very Large Scale Integration (vlsi) Systems
Low-Power, Highly Reliable Dynamic Thermal Management by Exploiting Approximate Computing
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With 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

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Publication Date
Tue Jan 01 2019
Journal Name
Australian Journal Of Mathematical Analysis And Applications
Formulation of approximate mathematical model for incoming water to some dams on Tigris and Euphrates Rivers using spline function
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n 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.

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Scopus
Publication Date
Sat Jul 20 2024
Journal Name
Journal Of Interdisciplinary Mathematics
Analytical solutions via coupled Elzaki adomian decomposition method for some applications
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An efficient combination of Adomian Decomposition iterative technique coupled Elzaki transformation (ETADM) for solving Telegraph equation and Riccati non-linear differential equation (RNDE) is introduced in a novel way to get an accurate analytical solution. An elegant combination of the Elzaki transform, the series expansion method, and the Adomian polynomial. The suggested method will convert differential equations into iterative algebraic equations, thus reducing processing and analytical work. The technique solves the problem of calculating the Adomian polynomials. The method’s efficiency was investigated using some numerical instances, and the findings demonstrate that it is easier to use than many other numerical procedures. It has

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Publication Date
Fri Mar 31 2017
Journal Name
Al-khwarizmi Engineering Journal
Comparative Study for Organic and Inorganic Draw Solutions in Forward Osmosis
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The present work aims to study forward osmosis process using different kinds of draw solutions and membranes. Three types of draw solutions (sodium chloride, sodium formate, and sodium acetate) were used in forward osmosis process to evaluate their effectiveness with respect to water flux and reverse salt flux. Experiments conducted in a laboratory-scale forward osmosis (FO) unit in cross flow flat sheet membrane cell.  Three types of membranes (Thin film composite (TFC), Cellulose acetate (CA), and Cellulose triacetate (CTA)) were used to determine the water flux under osmotic pressure as a driving force. The effect of temperature, draw solution concentration, feed and draw solution flow rate, and membrane types, were studied with

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