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.
In the literature, several correlations have been proposed for hold-up prediction in rotating disk contactor. However,
these correlations fail to predict hold-up over wide range of conditions. Based on a databank of around 611
measurements collected from the open literature, a correlation for hold up was derived using Artificial Neiral Network
(ANN) modeling. The dispersed phase hold up was found to be a function of six parameters: N, vc , vd , Dr , c d m / m ,
s . Statistical analysis showed that the proposed correlation has an Average Absolute Relative Error (AARE) of 6.52%
and Standard Deviation (SD) 9.21%. A comparison with selected correlations in the literature showed that the
developed ANN correlation noticeably
Orthogonal polynomials and their moments serve as pivotal elements across various fields. Discrete Krawtchouk polynomials (DKraPs) are considered a versatile family of orthogonal polynomials and are widely used in different fields such as probability theory, signal processing, digital communications, and image processing. Various recurrence algorithms have been proposed so far to address the challenge of numerical instability for large values of orders and signal sizes. The computation of DKraP coefficients was typically computed using sequential algorithms, which are computationally extensive for large order values and polynomial sizes. To this end, this paper introduces a computationally efficient solution that utilizes the parall
... Show MoreIn this paper, a computational method for solving optimal problem is presented, using indirect method (spectral methodtechnique) which is based on Boubaker polynomial. By this method the state and the adjoint variables are approximated by Boubaker polynomial with unknown coefficients, thus an optimal control problem is transformed to algebraic equations which can be solved easily, and then the numerical value of the performance index is obtained. Also the operational matrices of differentiation and integration have been deduced for the same polynomial to help solving the problems easier. A numerical example was given to show the applicability and efficiency of the method. Some characteristics of this polynomial which can be used for solvin
... Show MoreABSTRACT:In this paper, Cd10–xZnxS (x = 0.1, 0.3, 0.5) films were deposited by using chemical spray pyrolysis technique, the molar concentration precursor solution was 0.15 M/L. Depositions were done at 350°C on cleaned glass substrates. X-ray dif- fraction technique (XRD) studies for all the prepared film; all the films are crystalline with hexagonal structure .The optical properties of the prepared films were studied using measurements from VIS-UV-IR spectrophotometer at wave- length with the range 300 - 900 nm; the average transmission of the minimum doping ratio (Zn at 0.1%) was about 55% in the VIS region, it was decrease at the increasing of Zn concentration in the CdS films, The band gap of the doped CdS films was varied as 3.7, 3
... Show MoreFollowing model educational offenders in collection and Alasbaka of fifth grade students preparatory in history A. M. Dr Prepared by: Dr. Bashaer Mawloud Tawfeeq, The Center of Educational and Psychological Studies Baghdad University - There is no difference statistically significant at the 0.05 level of significance between the average scores of the following students studying using model and offenders and who are studying in the usual manner (traditional) in the collection - There is no difference statistically significant at the 0.05 level of significance between the mean scores for the following students studying using model and offenders and who are studying in the usual manner (traditional) in retention Find limits: Current search
... Show MoreMedia and communication's research are varied in accordance to research approaches' variety which seeks to reach convergent social, psychological, political, economic, and technical point of views. Its main aim is to assimilate all the new variables in the communicative method, especially, social media sites research; concerning their methodology, tools and theories. It is due to their diverse - developed applications and their increased rates of public use becoming irreplaceable in our daily life. It is well reflected by their consequent impact on the the public beside their role in changing its views.
This clarifies the notable increase of scientific research that concern them manifesting the dialectica
... Show MoreIf the Industrial Revolution has enabled the replacement of humans with machines, the digital revolution is moving towards replacing our brains with artificial intelligence, so it is necessary to consider how this radical transformation affects the graphic design ecosystem. Hence, the research problem emerged (what are the effects of artificial intelligence on graphic design) and the research aimed to know the capabilities and effects of artificial intelligence applications in graphic design, and the study dealt in its theoretical framework with two main axes, the first is the concept of artificial intelligence, and the second is artificial intelligence applications in graphic design. The descriptive approach adopted a method of content
... Show MoreIn this paper, the discriminant analysis is used to classify the most wide spread heart diseases known as coronary heart diseases into two groups (patient, not patient) based on the changes of discrimination features of ten predictor variables that we believe they cause the disease . A random sample for each group is employed and the stepwise procedures are performed in order to delete those variables that are not important for separating the groups. Tests of significance of discriminant analysis and estimating the misclassification rates are performed