Physics and applied mathematics form the basis for understanding natural phenomena using differential equations depicting the flow in porous media, the motion of viscous liquids, and the propagation of waves. These equations provide a thorough study of physical processes, enhancing the understanding of complex applications in engineering, technology, and medicine. This paper presents novel approximate solutions for the Darcy-Brinkmann-Forchheimer moment equation, the Blasius equation and the FalknerSkan equation with initial / boundary conditions by using two iterative methods: the variational iteration method and the optimal variational iteration method. The variational iteration method is effectively developed by adding a control paramete

This paper aims to find new analytical closed-forms to the  solutions of the nonhomogeneous functional differential equations of the n^th order with finite and constants delays and various initial delay conditions in terms of elementary functions using Laplace transform method. As well as, the definition of dynamical systems for ordinary differential equations is used to introduce the definition of dynamical systems for delay differential equations which contain multiple delays with a discussion of their dynamical properties: The exponential stability and strong stability

Friction Stir Welding (FSW) is one of the most effective solid states joining process and has numerous potential applications in many industries. A FSW numerical tool, based on ANSYS F.E software, has been developed. The amount of the heat gone to the tool dictates the life of the tool and the capability of the tool to produce a good processed zone. Hence, understanding the heat transfer aspect of the friction stir welding is extremely important for improving the process. Many research works were carried out to simulate the friction stir welding using various softwares to determine the temperature distribution for a given set of welding conditions. The objective of this research is to develop a finite element sim

In this current work, Purpose; to clearly the fundamental idea for constructing a design and
investigation of spur gear made of composite material its comes from the combination of (high
speeds, low noise, oil-les running, light weight, high strength, and more load capability)
encountered in modern engineering applications of the gear drives, when the usual metallic gear
cannot too overwhelming these combinations.
An analyzing of stresses and deformation under static and dynamic loading for spur gear tooth
by finite element method with isoparametric eight-nodded in total of 200 brick element with 340
nods in three degree of freedom per node was selected for this analysis. This is responsible for the
catastropic fa

The parametric programming considered as type of sensitivity analysis. In this research concerning to study the effect of the variations on linear programming model (objective function coefficients and right hand side) on the optimal solution. To determine the parameter (θ) value (-5≤ θ ≤5).Whereas the result، the objective function equal  zero and the decision variables are non basic، when the parameter (θ = -5).The objective function value increases when the parameter (θ= 5) and the decision variables are basic، with the except of X_24, X₃₄.Whenever the parameter value increase, the objectiv

 Film condensation of steam on a vertical tube is investigated numerically and experimentally,   in the present work. A mathematical model was set based on the basic conservation laws of mass   and energy, Nusselts analysis of film condensation, and empirical equations available in the   literature. Then, a simulation program in FORTRAN language was developed which simulates the   film condensation of steam on a vertical tube. A complete steam tables subprogram was also   developed and incorporated with the main program. The experimental work was carried out using a   steam condensation test bench. The inlet and outlet cooling water temperatures, steam temperature   and pressure, tube surface temperature at center, and co

In this paper, we describe the cases of marriage and divorce in the city of Baghdad on both sides of Rusafa and Karkh, we collected the data in this research from the Supreme Judicial Council and used the cubic spline interpolation method to estimate the function that passing through given points as well as the extrapolation method which was applied for estimating the cases of marriage and divorce for the next year and comparison between Rusafa and Karkh by using the MATLAB program.