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

The aim of this paper is to propose an efficient three steps iterative method for finding the zeros of the nonlinear equation f(x)=0 . Starting with a suitably chosen , the method generates a sequence of iterates converging to the root. The convergence analysis is proved to establish its five order of convergence. Several examples are given to illustrate the efficiency of the proposed new method and its comparison with other methods.

<p>Daftardar Gejji and Hossein Jafari have proposed a new iterative method for solving many of the linear and nonlinear equations namely (DJM). This method proved already the effectiveness in solved many of the ordinary differential equations, partial differential equations and integral equations. The main aim from this paper is to propose the Daftardar-Jafari method (DJM) to solve the Duffing equations and to find the exact solution and numerical solutions. The proposed (DJM) is very effective and reliable, and the solution is obtained in the series form with easily computed components. The software used for the calculations in this study was MATHEMATICA^® 9.0.</p>

Image steganography is undoubtedly significant in the field of secure multimedia communication. The undetectability and high payload capacity are two of the important characteristics of any form of steganography. In this paper, the level of image security is improved by combining the steganography and cryptography techniques in order to produce the secured image. The proposed method depends on using LSBs as an indicator for hiding encrypted bits in dual tree complex wavelet coefficient DT-CWT. The cover image is divided into non overlapping blocks of size (3*3). After that, a Key is produced by extracting the center pixel (pc) from each block to encrypt each character in the secret text. The cover image is converted using DT-CWT, then the p

Text based-image clustering (TBIC) is an insufficient approach for clustering related web images. It is a challenging task to abstract the visual features of images with the support of textual information in a database. In content-based image clustering (CBIC), image data are clustered on the foundation of specific features like texture, colors, boundaries, shapes. In this paper, an effective CBIC) technique is presented, which uses texture and statistical features of the images. The statistical features or moments of colors (mean, skewness, standard deviation, kurtosis, and variance) are extracted from the images. These features are collected in a one dimension array, and then genetic algorithm (GA) is applied for image clustering.

Porosity plays an essential role in petroleum engineering. It controls fluid storage in aquifers, connectivity of the pore structure control fluid flow through reservoir formations. To quantify the relationships between porosity, storage, transport and rock properties, however, the pore structure must be measured and quantitatively described. Porosity estimation of digital image utilizing image processing essential for the reservoir rock analysis since the sample 2D porosity briefly described. The regular procedure utilizes the binarization process, which uses the pixel value threshold to convert the color and grayscale images to binary images. The idea is to accommodate the blue regions entirely with pores and transform it to white in r