This paper sheds the light on the vital role that fractional ordinary differential equations(FrODEs) play in the mathematical modeling and in real life, particularly in the physical conditions. Furthermore, if the problem is handled directly by using numerical method, it is a far more powerful and efficient numerical method in terms of computational time, number of function evaluations, and precision. In this paper, we concentrate on the derivation of the direct numerical methods for solving fifth-order FrODEs in one, two, and three stages. Additionally, it is important to note that the RKM-numerical methods with two- and three-stages for solving fifth-order ODEs are convenient, for solving class's fifth-order FrODEs. Numerical examples have been analyzed to demonstrate the efficacy of the new methods in comparison to the analytical method. Therefore, the numerical compression is carried out to confirm the efficiency and precision of the modified numerical methods. Significantly, the study demonstrates that the numerical outcomes of the proposed derived and modified numerical applied methods proved to be brilliant. Finally, based on the findings of the study, it could be said that the numerical outcomes of the test-problems using proposed and modified methods agree well with the analytical solutions. Hence, we can conclude that the proposed numerical methods that are derived or modified in the analytic study of this paper are quite efficient.
The paper shows how to estimate the three parameters of the generalized exponential Rayleigh distribution by utilizing the three estimation methods, namely, the moment employing estimation method (MEM), ordinary least squares estimation method (OLSEM), and maximum entropy estimation method (MEEM). The simulation technique is used for all these estimation methods to find the parameters for the generalized exponential Rayleigh distribution. In order to find the best method, we use the mean squares error criterion. Finally, in order to extract the experimental results, one of object oriented programming languages visual basic. net was used
Receipt date:3/13/2021 accepted date:5/26/2021 Publication date:12/31/2021
This work is licensed under a Creative Commons Attribution 4.0 International License.
energy is one of the strategic resources within international politics, and this is through the existing competition between the international powers on it, and the global powers have begun to rely on interest in new areas, such as import, depending on new projects an
... Show MoreThe one-dimensional, spherical coordinate, non-linear partial differential equation of transient heat conduction through a hollow spherical thermal insulation material of a thermal conductivity temperature dependent property proposed by an available empirical function is solved analytically using Kirchhoff’s transformation. It is assumed that this insulating material is initially at a uniform temperature. Then, it is suddenly subjected at its inner radius with a step change in temperature. Four thermal insulation materials were selected. An identical analytical solution was achieved when comparing the results of temperature distribution with available analytical solution for the same four case studies that assume a constant thermal con
... Show MoreThe one-dimensional, cylindrical coordinate, non-linear partial differential equation of transient heat conduction through a hollow cylindrical thermal insulation material of a thermal conductivity temperature dependent property proposed by an available empirical
function is solved analytically using Kirchhoff’s transformation. It is assumed that this insulating material is initially at a uniform temperature. Then, it is suddenly subjected at its inner radius with a step change in temperature. Four thermal insulation materials were selected. An identical analytical solution was achieved when comparing the results of temperature distribution with available analytical solution for the same four case studies that assume a constant the
The behavior of externally prestressed composite beams under short term loading has been studied. A computer program developed originally by Oukaili to evaluate curvature is modified to evaluate the deflection of prestressed composite beam under flexural load. The analysis model based on the deformation compatibility of entire structure that allows to determine the full history of strain and stress distribution along cross section depth, deflection and stress increment in the external tendons .
The evaluation of curvatures for the composite beam involves iterations for computing the strains vectors at each node at any loading stage. The stress increment determined using equations depended on the member deflection at points of connecti
Iraq has the second largest proven oil reserves in the world. According to oil experts, it is expected that the Iraq's reserves to rise to 200+ billion barrels of high-grade crude.
Oil is a strategic commodity for producing and exporting countries in general, and Iraq in particular, as demonstrated by the international experience that oil is an important means to achieve economic growth, an important tool in the overall economic, social and political development. It is also an important source of hard currency for any national economy and a means to connect the local economy and the global economy. In this paper we focus our attention on selecting the best regression model that explain the effect of human capita
... Show MoreThis work is concerned with the study of the effect of cement types, particularly OPC and SRPC, which are the main cement types manufactured in Iraq. In addition, study the effect of mineral admixtures, which are HRM and SF on the resistance of high performance concrete (HPC) to internal sulphate attack. The HRM is used at (10%) and SF is used at (8 and 10)% as a partial replacement by weight of cement for both types. The percentages of sulphate investigated are (1,2 and 3)% by adding natural gypsum as a partial replacement by weight of fine aggregate. The tests carried out in this work are: compressive strength, flexural strength, ultrasonic pulse velocity, and density at the age of 7, 28, 90 and 120 days.
The r
... Show MoreIn this paper, we find the two solutions of two dimensional stochastic Fredholm integral equations contain two gamma processes differ by the parameters in two cases and equal in the third are solved by the Adomain decomposition method. As a result of the solutions probability density functions and their variances at the time t are derived by depending upon the maximum variances of each probability density function with respect to the three cases. The auto covariance and the power spectral density functions are also derived. To indicate which of the three cases is the best, the auto correlation coefficients are calculated.
In this paper we design a Simulink model which can be evaluate the concentration of Copper, Lead, Zinc, Cadmium, Cobalt, Nickel, Crum and Iron. So, this model would be a method to determine the contamination levels of these metals with the potential for this contamination sources with their impact. The aim of using Simulink environment is to solve differential equations individually and as given data in parallel with analytical mathematics trends. In general, mathematical models of the spread heavy metals in soil are modeled and solve to predict the behavior of the system under different conditions.
DEMs, thus, simply regular grids of elevation measurements over the land surface.The aim of the present work is to produce high resolution DEM for certain investigated region (i.e. Baghdad University Campus\ college of science). The easting and northing of 90 locations, including the ground-base and buildings of the studied area, have been obtained by field survey using global positioning system (GPS). The image of the investigated area has been extracted from Quick-Bird satellite sensor (with spatial resolution of 0.6 m). It has been geo-referenced and rectified using 1st order polynomial transformation. many interpolation methods have been used to estimate the elevation such as ordinary Kriging, inverse distance weight
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