Markov chains are an application of stochastic models in operation research, helping the analysis and optimization of processes with random events and transitions. The method that will be deployed to obtain the transient solution to a Markov chain problem is an important part of this process. The present paper introduces a novel Ordinary Differential Equation (ODE) approach to solve the Markov chain problem. The probability distribution of a continuous-time Markov chain with an infinitesimal generator at a given time is considered, which is a resulting solution of the Chapman-Kolmogorov differential equation. This study presents a one-step second-derivative method with better accuracy in solving the first-order Initial Value Problem

One of the most difficult issues in the history of communication technology is the transmission of secure images. On the internet, photos are used and shared by millions of individuals for both private and business reasons. Utilizing encryption methods to change the original image into an unintelligible or scrambled version is one way to achieve safe image transfer over the network. Cryptographic approaches based on chaotic logistic theory provide several new and promising options for developing secure Image encryption methods. The main aim of this paper is to build a secure system for encrypting gray and color images. The proposed system consists of two stages, the first stage is the encryption process, in which the keys are genera

The present work aims to study the efficiency of using aluminum refuse, which is available locally (after dissolving it in sodium hydroxide), with different coagulants like alum [Al2 (SO4)3.18H2O], Ferric chloride FeCl3 and polyaluminum chloride (PACl) to improve the quality of water. The results showed that using this coagulant in the flocculation process gave high results in the removal of turbidity as well as improving the quality of water by precipitating a great deal of ions causing hardness. From the experimental results of the Jar test, the optimum alum dosages are (25, 50 and 70 ppm), ferric chloride dosages are (15, 40 and 60 ppm) and polyaluminum chloride dosages were (10, 35 and 55 ppm) for initial water turbidity (100, 500 an

The research aims at demonstrating the role of the formulation of the green strategy in adopting the areas of the green strategy at the level of jobs in the municipal institutions in the province of Babylon, specifically the Directorate of the municipality of Hilla. The most important areas related to the green strategy were highlighted directly or indirectly, after the indicators of environmental damage emerged from the actions of companies and institutions. The research included a sample size of 222 individual of municipal institutions with different job titles and specializations between the technical and administrative and different levels of academic achievement within the institutions within the Ministry of Construction, Ho

     The primary objective of the current paper is to suggest and implement effective computational methods (DECMs) to calculate analytic and approximate solutions to the nonlocal one-dimensional parabolic equation which is utilized to model specific real-world applications. The powerful and elegant methods that are used orthogonal basis functions to describe the solution as a double power series have been developed, namely the Bernstein, Legendre, Chebyshev, Hermite, and Bernoulli polynomials. Hence, a specified partial differential equation is reduced to a system of linear algebraic equations that can be solved by using Mathematica®12. The techniques of effective computational methods (DECMs) have been applied to solve some s

In this study, an unknown force function dependent on the space in the wave equation is investigated. Numerically wave equation splitting in two parts, part one using the finite-difference method (FDM). Part two using separating variables method. This is the continuation and changing technique for solving inverse problem part in (1,2). Instead, the boundary element method (BEM) in (1,2), the finite-difference method (FDM) has applied. Boundary data are in the role of overdetermination data. The second part of the problem is inverse and ill-posed, since small errors in the extra boundary data cause errors in the force solution. Zeroth order of Tikhonov regularization, and several parameters of regularization are employed to decrease error

In our article, three iterative methods are performed to solve the nonlinear differential equations that represent the straight and radial fins affected by thermal conductivity. The iterative methods are the Daftardar-Jafari method namely (DJM), Temimi-Ansari method namely (TAM) and Banach contraction method namely (BCM) to get the approximate solutions. For comparison purposes, the numerical solutions were further achieved by using the fourth Runge-Kutta (RK4) method, Euler method and previous analytical methods that available in the literature. Moreover, the convergence of the proposed methods was discussed and proved. In addition, the maximum error remainder values are also evaluated which indicates that the propo