The purpose of this research paper is to present the second-order homogeneous complex differential equation   , where   , which is defined on the certain complex domain depends on solution behavior. In order to demonstrate  the relationship between the solution of the second-order of the complex differential equation and its coefficient of function, by studying the solution in certain cases: a meromorphic function, a coefficient of function, and if the solution is considered to be a transformation with another complex solution. In addition, the solution has been provided as a power series with some  applications.

The Ant System Algorithm (ASA) is a member of the ant colony algorithms family in swarm intelligence methods (part of the Artificial Intelligence field), which is based on the behavior of ants seeking a path and a source of food in their colonies. The aim of This algorithm is to search for an optimal solution for Combinational Optimization Problems (COP) for which is extremely difficult to find solution using the classical methods like linear and non-linear programming methods. 

The Ant System Algorithm was used in the management of water resources field in Iraq, specifically for Haditha dam which is one of the most important dams in Iraq. The target is to find out an efficient management system for

There Are Many  Communities Suffering Of Unemployment Due To Has  Great Social And Economic Impact, As Well As The Psychological Effects Devastating And Serious And That May Threaten States  With Collapse And  Leading Human Displacement And Loss And Crime, And Often Derive Unemployed People To Practice  Bad Habits Such As Gambling, Alcohol And Drug Abuse To Escape From Their Reality To Their Concerns And Problems.

It Should Be Noted, That The Largest Percentage Of Unemployment In Developing Societies Represented By The Educated Class Of University Graduates, And This Is Something Painful.

The Unemployed Know That (Each Capable Of Working And Who Want To Look For And Accept Prevailing Bricks) Is Th

In this article, we propose a Bayesian Adaptive bridge regression for ordinal model. We developed a new hierarchical model for ordinal regression in the Bayesian adaptive bridge. We consider a fully Bayesian approach that yields a new algorithm with tractable full conditional posteriors. All of the results in real data and simulation application indicate that our method is effective and performs very good compared to other methods. We can also observe that the estimator parameters in our proposed method, compared with other methods, are very close to the true parameter values.

Because the Coronavirus epidemic spread in Iraq, the COVID-19 epidemic of people quarantined due to infection is our application in this work. The numerical simulation methods used in this research are more suitable than other analytical and numerical methods because they solve random systems. Since the Covid-19 epidemic system has random variables coefficients, these methods are used. Suitable numerical simulation methods have been applied to solve the COVID-19 epidemic model in Iraq. The analytical results of the Variation iteration method (VIM) are executed to compare the results. One numerical method which is the Finite difference method (FD) has been used to solve the Coronavirus model and for comparison purposes. The numerical simulat

The main aim of this paper is to apply a new technique suggested by Temimi and Ansari namely (TAM) for solving higher order Integro-Differential Equations. These equations are commonly hard to handle analytically so it is request numerical methods to get an efficient approximate solution. Series solutions of the problem under consideration are presented by means of the Iterative Method (IM). The numerical results show that the method is effective, accurate and easy to implement rapidly convergent series to the exact solution with minimum amount of computation. The MATLAB is used as a software for the calculations.           

     The variational iteration method is used to deal with linear and nonlinear differential equations. The main characteristics of the method lie in its flexibility and ability to accurately and easily solve nonlinear equations. In this work, a general framework is presented for a variational iteration method for the analytical treatment of partial differential equations in fluid mechanics. The Caputo sense is used to describe fractional derivatives. The time-fractional Kaup-Kupershmidt (KK) equation is investigated, as it is the solution of the system of partial differential equations via the Boussinesq-Burger equation. By comparing the results that are obtained by the variational iteration method with those obtained by the two-dim

   In this work, a novel technique to obtain an accurate solutions to nonlinear form by multi-step combination with Laplace-variational approach (MSLVIM) is introduced. Compared with the  traditional approach for variational it overcome all difficulties and enable to provide us more an accurate solutions with extended of the convergence region as well as covering to larger intervals which providing us a continuous representation of approximate analytic solution and it give more better information of the solution over the whole time interval. This technique is more easier for obtaining the general Lagrange multiplier with reduces the time and calculations. It converges rapidly to exact formula with simply computable terms wit

In this paper, we deal with games of fuzzy payoffs problem while there is uncertainty in data. We use the trapezoidal membership function to transform the data into fuzzy numbers and utilize the three different ranking function algorithms. Then we compare between these three ranking algorithms by using trapezoidal fuzzy numbers for the decision maker to get the best gains

     This paper develop conventional Runge-Kutta methods of order four and order five to solve ordinary differential equations with oscillating solutions. The new modified Runge-Kutta methods (MRK) contain the invalidation of phase lag, phase lag’s derivatives, and amplification error. Numerical tests from their outcomes show the robustness and competence of the new methods compared to the well-known Runge-Kutta methods in the scientific literature.