This paper investigates an effective computational method (ECM) based on the standard polynomials used to solve some nonlinear initial and boundary value problems appeared in engineering and applied sciences. Moreover, the effective computational methods in this paper were improved by suitable orthogonal base functions, especially the Chebyshev, Bernoulli, and Laguerre polynomials, to obtain novel approximate solutions for some nonlinear problems. These base functions enable the nonlinear problem to be effectively converted into a nonlinear algebraic system of equations, which are then solved using Mathematica®12. The improved effective computational methods (I-ECMs) have been implemented to solve three applications involving nonlinear initial and boundary value problems: the Darcy-Brinkman-Forchheimer equation, the Blasius equation, and the Falkner-Skan equation, and a comparison between the proposed methods has been presented. Furthermore, the maximum error remainder () has been computed to prove the proposed methods' accuracy. The results convincingly prove that ECM and I-ECMs are effective and accurate in obtaining novel approximate solutions to the problems.
The aim of this paper is to design fast neural networks to approximate periodic functions, that is, design a fully connected networks contains links between all nodes in adjacent layers which can speed up the approximation times, reduce approximation failures, and increase possibility of obtaining the globally optimal approximation. We training suggested network by Levenberg-Marquardt training algorithm then speeding suggested networks by choosing most activation function (transfer function) which having a very fast convergence rate for reasonable size networks. In all algorithms, the gradient of the performance function (energy function) is used to determine how to
... Show MoreThere is a great deal of systems dealing with image processing that are being used and developed on a daily basis. Those systems need the deployment of some basic operations such as detecting the Regions of Interest and matching those regions, in addition to the description of their properties. Those operations play a significant role in decision making which is necessary for the next operations depending on the assigned task. In order to accomplish those tasks, various algorithms have been introduced throughout years. One of the most popular algorithms is the Scale Invariant Feature Transform (SIFT). The efficiency of this algorithm is its performance in the process of detection and property description, and that is due to the fact that
... Show MoreThe 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
... Show MoreThis study presents the execution of an iterative technique suggested by Temimi and Ansari (TA) method to approximate solutions to a boundary value problem of a 4th-order nonlinear integro-differential equation (4th-ONIDE) of the type Kirchhoff which appears in the study of transverse vibration of hinged shafts. This problem is difficult to solve because there is a non-linear term under the integral sign, however, a number of authors have suggested iterative methods for solving this type of equation. The solution is obtained as a series that merges with the exact solution. Two examples are solved by TA method, the results showed that the proposed technique was effective, accurate, and reliable. Also, for greater reliability, the approxim
... Show MoreThe feature extraction step plays major role for proper object classification and recognition, this step depends mainly on correct object detection in the given scene, the object detection algorithms may result with some noises that affect the final object shape, a novel approach is introduced in this paper for filling the holes in that object for better object detection and for correct feature extraction, this method is based on the hole definition which is the black pixel surrounded by a connected boundary region, and hence trying to find a connected contour region that surrounds the background pixel using roadmap racing algorithm, the method shows a good results in 2D space objects.
Keywords: object filling, object detection, objec
The availability of low- cost adsorbent namely Al-Khriet ( a substance found in the legs of Typha Domingensis) as an agricultural waste material, for the removal of lead and cadmium from aqueous solution was investigated. In the batch tests experimental parameters were studied, including adsorbent dosage between (0.2-1) g, initial metal ions concentration between (50-200) ppm (single and binary) and contact time (1/2-6) h. The removal percentage of each ion onto Al-Khriet reached equilibrium in about 4 hours. The highest adsorption capacity was for lead (96%) while for cadmium it was (90%) with 50 ppm ions concentration, 1 g dosage of adsorbent and pH 5.5. Adsorption capacity in the binary mixture were reduce at about 8% for lead a
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