The Wang-Ball polynomials operational matrices of the derivatives are used in this study to solve singular perturbed second-order differential equations (SPSODEs) with boundary conditions. Using the matrix of Wang-Ball polynomials, the main singular perturbation problem is converted into linear algebraic equation systems. The coefficients of the required approximate solution are obtained from the solution of this system. The residual correction approach was also used to improve an error, and the results were compared to other reported numerical methods. Several examples are used to illustrate both the reliability and usefulness of the Wang-Ball operational matrices. The Wang Ball approach has the ability to improve the outcomes by minimizing the degree of error between approximate and exact solutions. The Wang-Ball series has shown its usefulness in solving any real-life scenario model as first- or second-order differential equations (DEs).
In this work, a simple and new method is proposed to simultaneously improve the physical layer security and the transmission performance of the optical orthogonal frequency division multiplexing system, by combining orthogonal frequency division multiplexing technique with chaotic theory principles. In the system, a 2-D chaotic map is employed. The introduced system replaces complex operations such as matrix multiplication with simple operations such as multiplexing and inverting. The system performance in terms of bit error rate (BER) and peak to average ratio (PAPR) is enhanced. The system is simulated using Optisystem15 with a MATLAB2016 and for different constellations. The simulation results showed that the BE
... Show MoreExtreme conditions will cause the water level of high fill canal segment to change suddenly, which will affect the velocity and pore pressure of the slope. A 9 km irrigation earth canal in the city of Alsyahy, 15 km away from Al-Hilla city, and branching off from the left side of Shatt Al-Hilla at 57 km, was studied. The aim of this work is to study and analyze the effect of rationing system on the Birmana earthen canal during rapid drawdown case. Finite element modeling with Geo-Studio software was used in the present study to analyze the combined seepage and slope stability for three cycles. The resulting minimum safety factor obtained from the analysis using the saturated and
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And as a resul
... Show MoreVolterra – Fredholm integral equations (VFIEs) have a massive interest from researchers recently. The current study suggests a collocation method for the mixed Volterra - Fredholm integral equations (MVFIEs)."A point interpolation collocation method is considered by combining the radial and polynomial basis functions using collocation points". The main purpose of the radial and polynomial basis functions is to overcome the singularity that could associate with the collocation methods. The obtained interpolation function passes through all Scattered Point in a domain and therefore, the Delta function property is the shape of the functions. The exact solution of selective solutions was compared with the results obtained
... Show MoreTrickle irrigation is a system for supplying filtered water and fertilizer directly into the soil and water and it is allowed to dissipate under low pressure in an exact predetermined pattern. An equation to estimate the wetted area of unsaturated soil with water uptake by roots is simulated numerically using the HYDRUS-2D/3D software. In this paper, two soil types, which were different in saturated hydraulic conductivity were used with two types of crops tomato and corn, different values of emitter discharge and initial volumetric soil moisture content were assumed. It was assumed that the water uptake by roots was presented as a continuous sink function and it was introduced into Richard's equation in the unsaturated z
... Show MoreThe subject of multi- ethnics is one of the most important subjects in the study of political
geography, as multi- ethnics and its consequent problems are global geopolitical phenomena
that started early and reached its peak with the beginning of the twentieth century, because of
major changes in the political landscape that resulted by wars and led to the collapse of many
empires and major powers, a matter which led to put new political maps according to certain
considerations of the colonial powers, especially in Africa and Asia. All these things led to
the most serious challenges based on ethnic and sectarian conflict and led to the development
of geopolitical problems. Among the examples what most countries in th
This study presents a practical method for solving fractional order delay variational problems. The fractional derivative is given in the Caputo sense. The suggested approach is based on the Laplace transform and the shifted Legendre polynomials by approximating the candidate function by the shifted Legendre series with unknown coefficients yet to be determined. The proposed method converts the fractional order delay variational problem into a set of (n + 1) algebraic equations, where the solution to the resultant equation provides us the unknown coefficients of the terminated series that have been utilized to approximate the solution to the considered variational problem. Illustrative examples are given to show that the recommended appro
... Show MoreAn expression for the transition charge density is investigated where the deformation in nuclear collective modes is taken into consideration besides the shell model transition density. The inelastic longitudinal form factors C2 calculated using this transition charge density with excitation of the levels for Cr54,52,50 nuclei. In this work, the core polarization transition density is evaluated by adopting the shape of Tassie model together with the derived form of the ground state two-body charge density distributions (2BCDD's). It is noticed that the core polarization effects which represent the collective modes are essential in obtaining a remarkable agreement between the calculated inelastic longitudinal F(q)'s and those of experimen
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