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 specific cases of time-dependent diffusion equations. Moreover, the maximum absolute error () is determined to demonstrate the accuracy of the proposed techniques.
There are many diseases that affect the arteries, especially those related to their elasticity and stiffness, and they can be guessed by estimating and calculating the modulus of elasticity. Hence, the accurate calculation of the elastic modulus leads to an accurate assessment of these diseases, especially in their early stages, which can contribute to the treatment of these diseases early. Most of the calculations used the one-dimensional (1D) modulus of elasticity. From a mechanical point of view, the stresses to which the artery is subjected are not one-dimensional, but three-dimensional. Therefore, estimating at least a two-dimensional (2D) modulus of elasticity will necessarily be more accurate. To the knowledge of researchers, there i
... Show MoreThis study focuses on studying an oscillation of a second-order delay differential equation. Start work, the equation is introduced here with adequate provisions. All the previous is braced by theorems and examplesthat interpret the applicability and the firmness of the acquired provisions
This study has been performed for knowing the nutritional and chemical content of one kind chamomile tea for infant and children available in the pharmacy. The results have been showed that the percentage of essential compounds which represented with moisture, protein, fat, carbohydrate, ash and calories as 7.09%,0.01%,0.01%,92,81%, 0.08% and 371,37 Kal./100g, respectively of dry weight. Also the results have been showed that the percentage of chamomile plant extract that added to the tea as 5.74%. And the result of chemical test for effective materials in alcoholic extract showed consist Tannis, Glycosides, Flavonoids, Alkialoids,and Resins.
This paper is dealing with an experimental study to show the influence of the geometric characteristics of the vortex generators VG son the thickness of the boundary layer (∂) and drag coefficients (CD) of the flat plate. Vortex generators work effectively on medium and high angles of attack, since they are "hidden" under the boundary layer and practically ineffective at low angles.
The height of VGs relative to the thickness of the boundary layer enables us to study the efficacy of VGs in delaying boundary layer separation. The distance between two VGs also has an effect on the boundary layer if we take into
... Show MoreUnsaturated soil can raise many geotechnical problems upon wetting and drying resulting in swelling upon wetting and collapsing (shrinkage) in drying and changing in the soil shear strength. The classical principles of saturated soil are often not suitable in explaining these phenomena. In this study, expansive soil (bentonite and sand) were tested in different water contents and dry unit weight chosen from the compaction curve to examine the effect of water content change on soil properties (swelling pressure, expansion index, shear strength (soil cohesion) and soil suction by the filter paper method). The physical properties of these soils were studied by conducting series of tests in laboratory. Fitting methods
... Show MoreThe investigation of determining solutions for the Diophantine equation over the Gaussian integer ring for the specific case of is discussed. The discussion includes various preliminary results later used to build the resolvent theory of the Diophantine equation studied. Our findings show the existence of infinitely many solutions. Since the analytical method used here is based on simple algebraic properties, it can be easily generalized to study the behavior and the conditions for the existence of solutions to other Diophantine equations, allowing a deeper understanding, even when no general solution is known.