The nonlinear refractive index and the nonlinear absorption coefficient of unmodified and functional poly(methyl methacrylate) PMMA films were studied before and after the addition of the filler by the z-scan technique, using a Q-switched Nd:YAG laser at two wavelengths: 532 nm and 1064 nm, and at three input energies (13, 33 and 53) mJ. Both linear and nonlinear refractive indices and absorption coefficients of polymer films were studied by using UV-VIS spectrophotometer. The results show that the creation of functional PMMA from unmodified PMMA will increase the nonlinear optical properties in the functional PMMA/copper matrix more than in the unmodified PMMA/copper matrix. Hence, the functional PMMA appears promising as a useful third

MWCNTs and hybrid nanocomposite ZnO/Se/MWCNTs have been prepared via Solvothermal technique using Parr reactor at the temperature 180°C and SeCl2 as a catalyst. The obtained MWCNTs and ZnO/Se/MWCNTs are investigated using the FE-SEM, XRD, UV-VIS Spectroscopy and Z-Scan. The novelty of this research is studying the nonlinear optical properties for these prepared materials and the results exhibit that the thickness of the deposited film for hybrid nanocomposite ZnO/Se/MWCNTs is increased, which in turn, increase the nonlinear phase shift of the laser beam compared with the MWCNTs.

     The method of operational matrices is based on the Bernoulli and Shifted Legendre polynomials which is used to solve the Falkner-Skan equation. The nonlinear differential equation converting to a system of nonlinear equations is solved using Mathematica®12, and the approximate solutions are obtained. The efficiency of these methods was studied by calculating the maximum error remainder ( ), and it was found that their efficiency increases as  increases. Moreover, the obtained approximate solutions are compared with the numerical solution obtained by the fourth-order Runge-Kutta method (RK4), which gives  a good agreement.

The Korteweg-de Vries equation plays an important role in fluid physics and applied mathematics. This equation is a fundamental within study of shallow water waves. Since these equations arise in many applications and physical phenomena, it is officially showed that this equation has solitary waves as solutions, The Korteweg-de Vries equation is utilized to characterize a long waves travelling in channels. The goal of this paper is to construct the new effective frequent relation to resolve these problems where the semi analytic iterative technique presents new enforcement to solve Korteweg-de Vries equations. The distinctive feature of this method is, it can be utilized to get approximate solutions for travelling waves of 

In this paper, a discretization of a three-dimensional fractional-order prey-predator model has been investigated with Holling type III functional response. All its fixed points are determined; also, their local stability is investigated. We extend the discretized system to an optimal control problem to get the optimal harvesting amount. For this, the discrete-time Pontryagin’s maximum principle is used. Finally, numerical simulation results are given to confirm the theoretical outputs as well as to solve the optimality problem.

Krawtchouk polynomials (KPs) and their moments are promising techniques for applications of information theory, coding theory, and signal processing. This is due to the special capabilities of KPs in feature extraction and classification processes. The main challenge in existing KPs recurrence algorithms is that of numerical errors, which occur during the computation of the coefficients in large polynomial sizes, particularly when the KP parameter (p) values deviate away from 0.5 to 0 and 1. To this end, this paper proposes a new recurrence relation in order to compute the coefficients of KPs in high orders. In particular, this paper discusses the development of a new algorithm and presents a new mathematical model for computing the

Shatt Al-Hilla was considered one of the important branches of Euphrates River that supplies irrigation water to millions of dunams of planted areas. It is important to control the velocity and water level along the river to maintain the required level for easily diverting water to the branches located along the river. So, in this research, a numerical model was developed to simulate the gradually varied unsteady flow in Shatt AL-Hilla. The present study aims to solve the continuity and momentum (Saint-Venant) equations numerically to predict the hydraulic characteristics in the river using Galerkin finite element method. A computer program was designed and built using the programming language FORTRAN-77. Fifty kilometers was consid