In this paper Heun method has been used to find numerical solution for first order nonlinear functional differential equation. Moreover, this method has been modified in order to treat system of nonlinear functional differential equations .two numerical examples are given for conciliated the results of this method.
Abstract
Magnetic abrasive finishing (MAF) process is one of non-traditional or advanced finishing methods which is suitable for different materials and produces high quality level of surface finish where it uses magnetic force as a machining pressure. A set of experimental tests was planned according to Taguchi orthogonal array (OA) L27 (36) with three levels and six input parameters. Experimental estimation and optimization of input parameters for MAF process for stainless steel type 316 plate work piece, six input parameters including amplitude of tooth pole, and number of cycle between teeth, current, cutting speed, working gap, and finishing time, were performed by design of experiment
... Show MoreIn this paper, Touchard polynomials (TPs) are presented for solving Linear Volterra integral equations of the second kind (LVIEs-2k) and the first kind (LVIEs-1k) besides, the singular kernel type of this equation. Illustrative examples show the efficiency of the presented method, and the approximate numerical (AN) solutions are compared with one another method in some examples. All calculations and graphs are performed by program MATLAB2018b.
In this study, a new technique is considered for solving linear fractional Volterra-Fredholm integro-differential equations (LFVFIDE's) with fractional derivative qualified in the Caputo sense. The method is established in three types of Lagrange polynomials (LP’s), Original Lagrange polynomial (OLP), Barycentric Lagrange polynomial (BLP), and Modified Lagrange polynomial (MLP). General Algorithm is suggested and examples are included to get the best effectiveness, and implementation of these types. Also, as special case fractional differential equation is taken to evaluate the validity of the proposed method. Finally, a comparison between the proposed method and other methods are taken to present the effectiveness of the proposal meth
... Show MoreAbstract
In this work, two algorithms of Metaheuristic algorithms were hybridized. The first is Invasive Weed Optimization algorithm (IWO) it is a numerical stochastic optimization algorithm and the second is Whale Optimization Algorithm (WOA) it is an algorithm based on the intelligence of swarms and community intelligence. Invasive Weed Optimization Algorithm (IWO) is an algorithm inspired by nature and specifically from the colonizing weeds behavior of weeds, first proposed in 2006 by Mehrabian and Lucas. Due to their strength and adaptability, weeds pose a serious threat to cultivated plants, making them a threat to the cultivation process. The behavior of these weeds has been simulated and used in Invas
... Show More This research introduced the derivation of mathematical equations to calculate the Cartesian and geographical coordinates of a site situated at a far distance from the observer position by using GPS data. The geographical coordinates (ϕobs., λ obs., hobs.) for observer position were transformed to Cartesian coordinates (X obs., Y obs., Z obs.) of observer position itself. Then the Cartesian coordinates of unknown position mathematically were calculated from these calculated equations, and its transformed to geographical coordinates of (ϕunk., λunk.) position.
LandSat Satellite ETM+ image have been analyzed to detect the different depths of regions inside the Tigris river in order to detect the regions that need to remove sedimentation in Baghdad in Iraq Country. The scene consisted of six bands (without the thermal band), It was captured in March ٢٠٠١. The variance in depth is determined by applying the rationing technique on the bands ٣ and ٥. GIS ٩. ١ program is used to apply the rationing technique and determined the results.
In the present work, a z-scan technique was used to study the nonlinear optical properties, represented by the nonlinear refractive index and nonlinear absorption coefficients of nanoparticles cadmium sulfide thin film. The sample was prepared by the chemical bath deposition method. Several testing were done including, x-ray, transmission and thickness of thin film. z-Scan experiment was performed at two wavelengths (1064 nm and 532 nm) and different energies. The results showed the effect of self-focusing in the material at higher intensities, which evaluated n2 to be (0.11-0.16) cm2/GW. The effect of two-photon absorption was studied, which evaluated β to be (24-106) cm/GW. In addition, the optical limiting behavior has been studied.
... Show MoreThis study is unique in this field. It represents a mix of three branches of technology: photometry, spectroscopy, and image processing. The work treats the image by treating each pixel in the image based on its color, where the color means a specific wavelength on the RGB line; therefore, any image will have many wavelengths from all its pixels. The results of the study are specific and identify the elements on the nucleus’s surface of a comet, not only the details but also their mapping on the nucleus. The work considered 12 elements in two comets (Temple 1 and 67P/Churyumoy-Gerasimenko). The elements have strong emission lines in the visible range, which were recognized by our MATLAB program in the treatment of the image. The percen
... Show More