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>

Statistical methods and statistical decisions making were used to arrange and analyze the primary data to get norms which are used with Geographic Information Systems (GIS) and spatial analysis programs to identify the animals production and poultry units in strategic nutrition channels, also the priorities of food insecurity through the local production and import when there is no capacity for production. The poultry production is one of the most important commodities that satisfy human body protein requirements, also the most important criteria to measure the development and prosperity of nations. The poultry fields of Babylon Governorate are located in Abi Ghareg and Al_Kifil centers according to many criteria or factors such as the popu

Shatt Al-Hilla branches from the left of Euphrates River, U/S Hindiyah Barrage, Iraq, and extends about 100 km. It branches at the end into Shatt Al-Diwaniya 112 km and Shatt Al-Daghara 64 km. The study aims to evaluate and develop (Hilla-Daghara) rivers system, which is included Shatt Al-Hilla and Shatt Al-Daghara. Fieldwork began from (26 October until December) 2020. M9, S5 devices, and the installed staff gauges were used to measure discharges and water levels, respectively. A one-dimensional model was developed for the study area by HEC-RAS, after calibration and verification by field measurements; the Manning's n of Shatt Al-Daghara is found to be 0.022. Five Scenarios were simulated to study the reach under the cu