<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>

Praise be to God, Lord of the Worlds, and the best blessings and peace be upon our master Muhammad and all his family and companions, and those who follow them with goodness until the Day of Judgment. . And after:

God created man in the best manner, and subjugated the universe to him and favored him over the rest of creation when he gave him a mind to contemplate and know how to distinguish between the harmful and the beneficial, the bad and the good, in order to exploit him in achieving the meaning of worship, because it is the highest goal of his creation. God Almighty said (And I did not create the jinn and mankind. Except that they worship them.” [Al-Dhariyat: 56]

If knowing what is harmful from what is beneficial a

     A new mathematical model describing the motion of manned maneuvering targets is presented. This model is simple to be implemented and closely represents the motion of maneuvering targets. The target maneuver or acceleration is correlated in time. Optimal Kalman filter is used as a tracking filter which results in effective tracker that prevents the loss of track or filter divergency that often occurs with conventional tracking filter when the target performs a moderate or heavy maneuver. Computer simulation studies show that the proposed tracker provides sufficient accuracy.

This research presents and discuss the results of experimental investigation carried out on geogrids model to study the behavior of geogrid in the loose sandy soil. The effect of location eccentricity, depth of first layer of reinforcement, vertical spacing, number and type of reinforcement layers have been investigated. The results indicated that the percentage of bearing improvement a bout (22 %) at number of reinforced layers N=1 and about (47.5%) at number of reinforced layers N=2 for different Eccentricity values when depth ratio and vertical spacing between layers are (0.5B and 0.75B) respectively

Two-dimensional unsteady mixed convection in a porous cavity with heated bottom wall is numerically studied in the present paper. The forced flow conditions are imposed by providing a hydrostatic pressure head at the inlet port that is located at the bottom of one of the vertical side walls and an open vent at the top of the other vertical side wall. The Darcy model is adopted to model the fluid flow in the porous medium and the combination effects of hydrostatic pressure head and the heat flux quantity parameters are carefully investigated. These governing parameters are varied over wide ranges and their effect on the heat transfer characteristics is studied in detail. It is found that the time required to reach a desired temperature at th

Simulation of free convection heat transfer in a square enclosure induced by heated thin plate is represented numerically. All  the enclosure walls have constant temperature lower than the plate’s temperature. The flow is assumed to be two-dimensional. The discretized equations were solved stream function, vorticity, and energy equations by finite difference method using explicit technique and Successive Over- Relaxation method. The study was performed for different values of Rayleigh number ranging from 10³ to 10⁵ for different angle position of heated thin plate(0°, 45°, 90°). Air was chosen as a working fluid (Pr = 0.71). Aspect ratio of center of plate to the parallel left wall A₂

The research aims to develop physical exercises with auxiliary training tools that work to develop the explosive power of the arms and legs, and then find out their effect on the accuracy of shooting from free throw and correction from jumping of advanced basketball players, as the researchers found a problem that these players have weakness in the skill of throwing Free throwing and shooting by jumping calculated with two points as a result of adopting unhealthy physical and technical positions, which led to a lack of focus and accuracy, and thus negatively affected the performance technique of free throw and jump shot, as most teams use traditional exercises without the use of auxiliary training tools, and this topic gave researchers the

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In this paper a modified approach have been used to find the approximate solution of ordinary delay differential equations with constant delay using the collocation method based on Bernstien polynomials.