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.

Many problems were encountered during the drilling operations in Zubair oilfield. Stuckpipe, wellbore instability, breakouts and washouts, which increased the critical limits problems, were observed in many wells in this field, therefore an extra non-productive time added to the total drilling time, which will lead to an extra cost spent. A 1D Mechanical Earth Model (1D MEM) was built to suggest many solutions to such types of problems. An overpressured zone is noticed and an alternative mud weigh window is predicted depending on the results of the 1D MEM. Results of this study are diagnosed and wellbore instability problems are predicted in an efficient way using the 1D MEM. Suitable alternative solutions are presented

An analytical expression for the charge density distributions is derived based on the use of occupation numbers of the states and the single particle wave functions of the harmonic oscillator potential with size parameters chosen to reproduce the observed root mean square charge radii for all considered nuclei. The derived expression, which is applicable throughout the whole region of shell nuclei, has been employed in the calculations concerning the charge density distributions for odd- of shell nuclei, such as and nuclei. It is found that introducing an additional parameters, namely and which reflect the difference of the occupation numbers of the states from the prediction of the simple shell model leads to obtain a remarkabl

We investigate the interaction of proton with a solid target, describing the wake effects by taking fitted parameters with experimental values of energy loss function ELF for copper using the dielectric function of random phase approximation (RPA). The results exhibited a damped oscillatory behavior in the longitudinal direction behind the projectile. In addition, the wake potential becomes asymmetric around the z-axis with proton velocity values higher than Fermi velocity, as well as it depends on the position of projectile in cylindrical coordinates.

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