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

        In this paper, an estimate has been made for parameters and the reliability function for Transmuted power function (TPF) distribution through using some estimation methods as proposed new technique for white, percentile, least square, weighted least square and modification moment methods. A simulation was used to generate random data that follow the (TPF) distribution on three experiments (E₁ , E₂ , E₃)  of the real values of the parameters, and with sample size (n=10,25,50 and 100) and iteration samples (N=1000), and taking reliability times (0< t < 0) . Comparisons have been made between the obtained results from the estimators using mean square error (MSE). The results showed the

Inherent fluctuations in the availability of energy from renewables, particularly solar, remain a substantial impediment to their widespread deployment worldwide. Employing phase-change materials (PCMs) as media, saving energy for later consumption, offers a promising solution for overcoming the problem. However, the heat conductivities of most PCMs are limited, which severely limits the energy storage potential of these materials. This study suggests employing circular fins with staggered distribution to achieve improved thermal response rates of PCM in a vertical triple-tube heat exchanger involving two opposite flow streams of the heat-transfer fluid (HTF). Since heat diffusion is not the same at various portions of the PCM unit,

This study explored the feasibility of removing nickel (Ni) and Pb (II) from water solutions using the adsorption technique by cellulose recovered from office paper waste. Metal removal is required to reduce the direct or indirect exposure of industrial waste to the environment, due to its potential for harm to human health and ecosystems. The release criterion is maintained to keep the efficient wastewater treatment of the metals of concern, which are toxic to both humans and other organisms. The cellulose was first prepared from office paper waste. The removal values can be rationalized as follows: Lead removal efficiencies of were obtained upto %95.0632, while the removals of nickel were obtained as 54.3866%. The adsorption proce

The aim of this study is to propose mathematical expressions for estimation of the flexural strength of plain concrete members from ultrasonic pulse velocity (UPV) measurements. More than two hundred pieces of precast concrete kerb units were subjected to a scheduled test program. The tests were divided into two categories; non-destructive ultrasonic and bending or rupture tests. For each precast unit, direct and indirect (surface) ultrasonic pulses were subjected to the concrete media to measure their travel velocities. The results of the tests were monitored in two graphs so that two mathematical relationships can be drawn. Direct pulse velocity versus the flexural strength was given in the first relationship while the second equation des

KE Sharquie, AA Noaimi, SY Mohsin, 2011 - Cited by 4

The aim of this study is to propose mathematical expressions for estimation of the flexural strength of plain concrete members from ultrasonic pulse velocity (UPV) measurements. More than two hundred
pieces of precast concrete kerb units were subjected to a scheduled test program. The tests were divided into two categories; non-destructive ultrasonic and bending or rupture tests. For each precast unit, direct and indirect (surface) ultrasonic pulses were subjected to the concrete media to measure their travel velocities. The results of the tests were mointered in two graphs so that two mathematical relationships can be drawn. Direct pulse velocity versus the flexural strength was given in the first relationship while the second equati

This work is concerned with the vibration attenuation of a smart beam interacting with fluid using proportional-derivative PD control and adaptive approximation compensator AAC. The role of the AAC is to improve the PD performance by compensating for unmodelled dynamics using the concept of function approximation technique FAT. The key idea is to represent the unknown parameters using the weighting coefficient and basis function matrices/vectors. The weighting coefficient vector is updated using Lyapunov theory. This controller is applied to a flexible beam provided with surface bonded piezo-patches while the vibrating beam system is submerged in a fluid. Two main effects are considered: 1) axial stretching of the vibrating beam that leads