This paper considers approximate solution of the hyperbolic one-dimensional wave equation with nonlocal mixed boundary conditions by improved methods based on the assumption that the solution is a double power series based on orthogonal polynomials, such as Bernstein, Legendre, and Chebyshev. The solution is ultimately compared with the original method that is based on standard polynomials by calculating the absolute error to verify the validity and accuracy of the performance.

     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

Hard water does not pose a threat to human health but may cause precipitation of soap or results stone in the boilers. These reactions are caused by the high concentrations of Ca and Mg. In the industry they are undesirable because of higher fuel consumption for industrial use .Electromagnetic polarization water treatment is a method which can be used for increasing the precipitation of Ca ²⁺ and CO₃ ^2- ions in hard water to form CaCO₃ which leads to decrease the water hardness is research has been conducted by changing the number of coil turns and voltage of the system. The spectroscopy electron microscope was used for imaging the produced crystals. Results of the investigation indicated that

Many purposes require communicating audio files between the users using different applications of social media. The security level of these applications is limited; at the same time many audio files are secured and must be accessed by authorized persons only, while, most present works attempt to hide single audio file in certain cover media. In this paper, a new approach of hiding three audio signals with unequal sizes in single color digital image has been proposed using the frequencies transform of this image. In the proposed approach, the Fast Fourier Transform was adopted where each audio signal is embedded in specific region with high frequencies in the frequency spectrum of the cover image to sa

In this paper we use Bernstein polynomials for deriving the modified Simpson's 3/8 , and the composite modified Simpson's 3/8 to solve one dimensional linear Volterra integral equations of the second kind , and we find that the solution computed by this procedure is very close to exact solution.

The Assignment model is a mathematical model that aims to express a real problem facing factories and companies which is characterized by the guarantee of its activity in order to make the appropriate decision to get the best allocation of machines or jobs or workers on machines in order to increase efficiency or profits to the highest possible level or reduce costs or time To the extent possible, and in this research has been using the method of labeling to solve the problem of the fuzzy assignment of real data has been approved by the tire factory Diwaniya, where the data included two factors are the factors of efficiency and cost, and was solved manually by a number of iterations until reaching the optimization solution,