This manuscript presents several applications for solving special kinds of ordinary and partial differential equations using iteration methods such as Adomian decomposition method (ADM), Variation iterative method (VIM) and Taylor series method. These methods can be applied as well as to solve nonperturbed problems and 3rd order parabolic PDEs with variable coefficient. Moreover, we compare the results using ADM, VIM and Taylor series method. These methods are a commination of the two initial conditions.

Darcy-Weisbach (D-W) is a typical resistance equation in pressured flow; however, some academics and engineers prefer Hazen-Williams (H-W) for assessing water distribution networks. The main difference is that the (D-W) friction factor changes with the Reynolds number, while the (H-W) coefficient is a constant value for a certain material. This study uses WaterGEMS CONNECT Edition update 1 to find an empirical relation between the (H-W) and (H-W) equations for two 400 mm and 500 mm pipe systems. The hydraulic model was done, and two scenarios were applied by changing the (H-W) coefficient to show the difference in results of head loss. The results showed a strong relationship between both equations with correlation coefficients of 0.999,

This research sheds light on those discrepancies in the use of ornaments, adornment and perfumes, as well as the art of cosmetics, in two important civilizations, namely, the Mesopotamian civilization as the earlier civilization, and the civilization of Yemen, which represents the first Arab civilization. Through the foregoing, our research includes two topics, the first topic included the history of the use of decorations, ornaments and perfumes in the civilization of Mesopotamia, while the second topic included the study of ornaments, adornment and cosmetic art in the ancient civilization of Yemen. And then the research came out with a number of conclusions that the researcher considers very important to highlight the differences and f

Receipt date:2/17/2021 acceptance date:3/16/2021 Publishing date:12/31/2021

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Objective: This paper investigates the contradictions in the decision-making process of the United States, which historically proven to be successful policies in the short term, but in the long term proven to be wanting and failure. Methodology: The paper uses descriptive, historical, comparative method. A

The aim of our study is to solve a nonlinear epidemic model, which is the COVID-19 epidemic model in Iraq, through the application of initial value problems in the current study. The model has been presented as a system of ordinary differential equations that has parameters that change with time. Two numerical simulation methods are proposed to solve this model as suitable methods for solving systems whose coefficients change over time. These methods are the Mean Monte Carlo Runge-Kutta method (MMC_RK) and the Mean Latin Hypercube Runge-Kutta method (MLH_RK). The results of numerical simulation methods are compared with the results of the numerical Runge-Kutta 4th order method (RK4) from 2021 to 2025 using the absolute error, which prove

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