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.

The aim of this book is to present a method for solving high order ordinary differential equations with two point boundary condition of the different kind, we propose semi-analytic technique using two-point osculatory interpolation to construct polynomial solution. The original problem is concerned using two-points osculatory interpolation with the fit equal numbers of derivatives at the end points of an interval [0 , 1] . Also, we discussion the existence and uniqueness of solutions and many examples are presented to demonstrate the applicability, accuracy and efficiency of the methods by compared with conventional method .i.e. VIDM , Septic B-Spline , , NIM , HPM, Haar wavelets on one hand and to confirm the order convergence on the other

Several attempts have been made to modify the quasi-Newton condition in order to obtain rapid convergence with complete properties (symmetric and positive definite) of the inverse of  Hessian matrix (second derivative of the objective function). There are many unconstrained optimization methods that do not generate positive definiteness of the inverse of Hessian matrix. One of those methods is the symmetric rank 1( H-version) update (SR1 update), where this update satisfies the quasi-Newton condition and the symmetric property of inverse of Hessian matrix, but does not preserve the positive definite property of the inverse of Hessian matrix where the initial inverse of Hessian matrix is positive definiteness. The positive definite prope

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 study, the electron coefficients; Mean energy , Mobility and Drift velocity  of different gases  Ar, He, N₂ and O₂  in the  ionosphere have been calculated using BOLSIG+ program to check the solution results of Boltzmann equation results, and effect of reduced electric field (E/N) on electronic coefficients. The electric field has been specified in the limited range 1-100 Td. The gases were in the ionosphere layer at an altitude frame 50-2000 km. Furthermore, the mean energy and drift velocity steadily increased with increases in the electric field, while mobility was reduced. It turns out that there is a significant and obvious decrease in mobility as a result of inelastic collisions and in addition lit

The aim of our study is to reveal the effect of steel reinforcement details,tensile steel reinforcement ratio, compressed reinforcing steel ratio,reinforcing steel size, corner joint shape on the strength of reinforcedconcrete Fc' and delve into it for the most accurate details and concreteconnections about the behavior and resistance of the corner joint ofreinforced concrete, Depending on the available studies and sources inaddition to our study, we concluded that each of these effects had a clearrole in the behavior and resistance of the corner joint of reinforced concreteunder the influence of the negative moment and yield stress. A studyof the types of faults that can be reinforced angle joints obtains detailsand conditions of c

In this paper, the proposed phase fitted and amplification fitted of the Runge-Kutta-Fehlberg method were derived on the basis of existing method of 4(5) order to solve ordinary differential equations with oscillatory solutions. The recent method has null phase-lag and zero dissipation properties. The phase-lag or dispersion error is the angle between the real solution and the approximate solution. While the dissipation is the distance of the numerical solution from the basic periodic solution. Many of problems are tested over a long interval, and the numerical results have shown that the present method is more precise than the 4(5) Runge-Kutta-Fehlberg method.

In this paper Volterra Runge-Kutta methods which include: method of order two and four will be applied to general nonlinear Volterra integral equations of the second kind. Moreover we study the convergent of the algorithms of Volterra Runge-Kutta methods. Finally, programs for each method are written in MATLAB language and a comparison between the two types has been made depending on the least square errors.

In this paper the modified trapezoidal rule is presented for solving Volterra linear Integral Equations (V.I.E) of the second kind and we noticed that this procedure is effective in solving the equations. Two examples are given with their comparison tables to answer the validity of the procedure.