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.

Many numerical approaches have been suggested to solve nonlinear problems. In this paper, we suggest a new two-step iterative method for solving nonlinear equations. This iterative method has cubic convergence. Several numerical examples to illustrate the efficiency of this method by Comparison with other similar methods is given.

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, we consider a new approach to solve type of partial differential equation by using coupled Laplace transformation with decomposition method to find the exact solution for non–linear non–homogenous equation with initial conditions. The reliability for suggested approach illustrated by solving model equations such as second order linear and nonlinear Klein–Gordon equation. The application results show the efficiency and ability for suggested approach.

     In this article, a new efficient approach is presented to solve a type of partial differential equations, such (2+1)-dimensional differential equations non-linear, and nonhomogeneous. The procedure of the new approach is suggested to solve important types of differential equations and get accurate analytic solutions i.e., exact solutions. The effectiveness of the suggested approach based on its properties compared with other approaches has been used to solve this type of differential equations such as the Adomain decomposition method, homotopy perturbation method, homotopy analysis method, and variation iteration method. The advantage of the present method has been illustrated by some examples.

The research aimed to prepare a measure to evaluate the academic achievement of graduates working in the field of physical education from their point of view, to identify the extent to which graduating students benefit from the curriculum of the College of Physical Education and Sports Sciences, University of Baghdad/Al-Jadriya, and to identify the impact of academic subjects in the practical and theoretical fields. The researchers used the descriptive approach in the research procedures as it is an appropriate approach in achieving the research objectives. The following questions are: What are the academic subjects that have the most impact on graduating students? What are the academic subjects that have the least impact on the are

The research aimed to prepare a measure to evaluate the academic achievement of graduates working in the field of physical education from their point of view, to identify the extent to which graduating students benefit from the curriculum of the College of Physical Education and Sports Sciences, University of Baghdad/Al-Jadriya, and to identify the impact of academic subjects in the practical and theoretical fields. The researchers used the descriptive approach in the research procedures as it is an appropriate approach in achieving the research objectives. The following questions are: What are the academic subjects that have the most impact on graduating students? What are the academic subjects that have the least impact on the are