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).
An approximate solution of the liner system of ntegral cquations fot both fredholm(SFIEs)and Volterra(SIES)types has been derived using taylor series expansion.The solusion is essentailly
In this paper, a new class of non-convex functions called semi strongly (
Cardiovascular disease is one of the most common comorbidities associated with enlarged extremities, occurring in 60 % of patients with acromegaly. The aim of this study is to evaluate the relationship of growth hormone and insulin such as growth factor-1 with obesity, dyslipidemia, hyperglycemia, and pro-inflammatory cytokines (IL-2, IL-6, IL-10), as risk factors for cardiovascular disorder in acromegaly patients. Eighty subjects were included and categorized into two groups: 40 acromegaly patients and 40 of the control group. The results indicated weight excess, hyperglycemia, hypertension, lipid disorder, and elevated levels of interleukins (2, 6, and 10). The correlation of both GH and IGF-1 with each of weight, BMI, systolic blood p
... Show MoreMany cities suffer from the large spread of slums, especially the cities of the Middle East. The purpose of the paper is to study the reality of informal housing in Al-Barrakia and the most important problems that it suffers from. The paper also seeks to study the presence or absence of a correlation between urban safety indicators and urban containment indicators as one of the methods of developing and planning cities. This can be achieved through sustainable urban management. The slums are a source of many urban problems that threaten the security and safety of the residents and represent a focus for the concentration of crimes and drugs. The paper seeks to answer the following question: How can urban safety be improved through urban cont
... Show MoreThe approach given in this paper leads to numerical methods to find the approximate solution of volterra integro –diff. equ.1st kind. First, we reduce it from integro VIDEs to integral VIEs of the 2nd kind by using the reducing theory, then we use two types of Non-polynomial spline function (linear, and quadratic). Finally, programs for each method are written in MATLAB language and a comparison between these two types of Non-polynomial spline function is made depending on the least square errors and running time. Some test examples and the exact solution are also given.
This paper analyzes a piled-raft foundation on non-homogeneous soils with variable layer depth percentages. The present work aims to perform a three-dimensional finite element analysis of a piled-raft foundation subjected to vertical load using the PLAXIS 3D software. Parametric analysis was carried out to determine the effect of soil type and initial layer thickness. The parametric study showed that increasing the relative density from 30 % to 80 % of the upper sand layer and the thickness of the first layer has led to an increase in the ultimate load and a decrease in the settlement of piled raft foundations for the cases of sand over weak soil. In clay over weak soil, the ultimate load of the piled raft foundation w
... Show MoreExperimental and numerical studies have been conducted on the effects of bed roughness elements such as cubic and T-section elements that are regularly half-channel arrayed on one side of the river on turbulent flow characteristics and bed erosion downstream of the roughness elements. The experimental study has been done for two types of bed roughness elements (cubic and T-section shape) to study the effect of these elements on the velocity profile downstream the elements with respect to different water flow discharges and water depths. A comparison between the cubic and T-section artificial bed roughness showed that the velocity profile downstream the T-section increased in smooth side from the river and decrease in the rough side
... Show MoreFriction Stir Welding (FSW) is one of the most effective solid states joining process and has numerous potential applications in many industries. A FSW numerical tool, based on ANSYS F.E software, has been developed. The amount of the heat gone to the tool dictates the life of the tool and the capability of the tool to produce a good processed zone. Hence, understanding the heat transfer aspect of the friction stir welding is extremely important for improving the process. Many research works were carried out to simulate the friction stir welding using various softwares to determine the temperature distribution for a given set of welding conditions. The objective of this research is to develop a finite element sim
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