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.

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.

     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 

This research is an initial attempt to explore the reality of reform and its concept in Islam, and to describe the presence of educational practices in the Arab-Islamic heritage. The importance of this research lies in addressing a number of important issues related to the contemporary Islamic reform system. The research showed the need for authentic educational reform values that draw their reference from the origins of Islam. The research also emphasized the analysis of the reality of education in the Muslim world and the identification of its problems and the search for solutions through a quick and comprehensive look at the diverse contributions of Muslim thinkers to Islamic educational reform thought, and their active role in addressin

Crime is one of the most severe challenges facing States, and strives to find preventive measures, reduce its seriousness, and prevent them; due to developments, crimes have increased, and emerging new patterns of crimes, there is an urgent need to prevent crimes and reduce their effects. Modernizing its punitive system and diverting it to correctional rehabilitative justice to redress the prejudice caused by the crime and rehabilitate the convicted person by using alternative measures to short-term imprisonment. This research emphasizes alternative sanctions' value to minimizing short-term imprisonment penalties and their impact on societal security through several goals like, the negative consequences, justifications, and alternatives