The aim of this article is to solve the Volterra-Fredholm integro-differential equations of fractional order numerically by using the shifted Jacobi polynomial collocation method. The Jacobi polynomial and collocation method properties are presented. This technique is used to convert the problem into the solution of linear algebraic equations. The fractional derivatives are considered in the Caputo sense. Numerical examples are given to show the accuracy and reliability of the proposed technique.
For many problems in Physics and Computational Fluid Dynamics (CFD), providing an accurate approximation of derivatives is a challenging task. This paper presents a class of high order numerical schemes for approximating the first derivative. These approximations are derived based on solving a special system of equations with some unknown coefficients. The construction method provides numerous types of schemes with different orders of accuracy. The accuracy of each scheme is analyzed by using Fourier analysis, which illustrates the dispersion and dissipation of the scheme. The polynomial technique is used to verify the order of accuracy of the proposed schemes by obtaining the error terms. Dispersion and dissipation errors are calculated
... Show MoreThis paper deals with an analytical study of the flow of an incompressible generalized Burgers’ fluid (GBF) in an annular pipe. We discussed in this problem the flow induced by an impulsive pressure gradient and compare the results with flow due to a constant pressure gradient. Analytic solutions for velocity is earned by using discrete Laplace transform (DLT) of the sequential fractional derivatives (FD) and finite Hankel transform (FHT). The influences of different parameters are analyzed on a velocity distribution characteristics and a comparison between two cases is also presented, and discussed in details. Eventually, the figures are plotted to exhibit these effects.
Construction projects have become a changing dramatically in recent decades and that the goal of the beneficiaries of the implementation of structural project is to complete the work with less time and within the cost of the specific and the best possible quality may sometimes happen that highlights the importance of time on the rest of the items at the implementation of projects for various reasons, including the need to use the project as soon as possible possible change rapidly to customer's requests, but the high cost of the project represents the biggest obstacle for entrepreneurs with its effects on the quality and the time workers, and is a measure of those elements in monetary terms is the key to integration between them, so the
... Show MoreThe present work describes numerical and experimental investigation of the heat transfer characteristics in a plate-fin, having built-in piezoelectric actuator mounted on the base plate (substrate). The geometrical configuration considered in the present work is representative of a single element of the plate-fin and triple fins. Air is taken as the working fluid. A performance data for a single rectangular fin and triple fins are provided for different frequency levels (5, 30 and
50HZ) , different input power (5,10,20,30,40 and 50W) and different inlet velocity (0.5, 1, 2, 3, 4, 5 and 6m/s) for the single rectangular fin and triple fins with and without oscillation. The investigation was also performed with different geometrical fin
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A simple reverse-phase high performance liquid chromatographic method for the simultaneous analysis (separation and quantification) of furosemide (FURO), carbamazepine (CARB), diazepam (DIAZ) and carvedilol (CARV) has been developed and validated. The method was carried out on a NUCLEODUR® 100-5 C18ec column (250 x 4.6 mm, i. d.5μm), with a mobile phase comprising of acetonitrile: deionized water (50: 50 v/v, pH adjusted to 3.6 ±0.05 with acetic acid) at a flow rate 1.5 mL.min-1 and the quantification was achieved at 226 nm. The retention times of FURO, CARB, DIAZ and CARV were found to be 1.90 min, 2.79 min, 5.39 min and 9.56 min respectively. The method was validated in terms of linearity, accuracy, precision, limit of detection and li
... Show MoreAbstract. In this scientific work, we investigate the problem of the practical necessity of achieving the adequacy of translation activities with active translation from Russian into Arabic in various fields of translation. Based on the material of the latest suffix vocabulary, a serious attempt is made to clarify and specify the rules for the development of translator's intuition when translating from Russian into Arabic and vice versa. Based on the material collected by the latest suffix vocabulary, we try to make an attempt to reveal the role of suffix word creation in highlighting the general rules for achieving translation equivalence. The paper examines the process of creating words in multi-family languages, the difference between th
... Show MoreAccurate predictive tools for VLE calculation are always needed. A new method is introduced for VLE calculation which is very simple to apply with very good results compared with previously used methods. It does not need any physical property except each binary system need tow constants only. Also, this method can be applied to calculate VLE data for any binary system at any polarity or from any group family. But the system binary should not confirm an azeotrope. This new method is expanding in application to cover a range of temperature. This expansion does not need anything except the application of the new proposed form with the system of two constants. This method with its development is applied to 56 binary mixtures with 1120 equili
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