The derivation of 5^th order diagonal implicit type Runge Kutta methods (DITRKM5) for solving 3^rd special order ordinary differential equations (ODEs) is introduced in the present study. The DITRKM5 techniques are the name of the approach. This approach has three equivalent non-zero diagonal elements. To investigate the current study, a variety of tests for five various initial value problems (IVPs) with different step sizes h were implemented. Then, a comparison was made with the methods indicated in the other literature of the implicit RK techniques. The numerical techniques are elucidated as the qualification regarding the efficiency and number of function evaluations compared with another literature of the implic

Many countries are very important in their interest not only in diversifying foreign reserves, but in determining and planning their volume in accordance with the goals set, namely facing potential external shocks, as the research aims to determine the extent of the strength of foreign reserves in the possession of the Central Bank in relation to every influential variable in the Iraqi economy. , in order to determine the minimum level of reserves that requires reconsideration of the exchange rate, as the research adopted the inductive analytical method in analyzing real (Quantitative data) for the research variables in the years of study, as the research adopted a set of analytical indicators approved by the International Moneta

     In this paper, our aim is to solve analytically a nonlinear social epidemic model as an initial value problem (IVP) of ordinary differential equations. The mathematical social epidemic model under study is applied to alcohol consumption model in Spain. The economic cost of alcohol consumption in Spain is affected by the amount of alcohol consumed. This paper refers to the study of alcohol consumption using some analytical methods. Adomian decomposition and variation iteration methods for solving alcohol consumption model have used. Finally, a compression between the analytic solutions of the two used methods and the previous actual values from 1997 to 2007 years is obtained using the absolute and

In this paper, we investigate and study quantum theoretical of quark-gluon interaction modeling in QGP matter formatted. In theoretical modeling, we can use a flavor number, strength coupling, critical energy Tc = 190 MeV, system energy (400-650)MeV, fugacity of quark and gluon, and photon energy in range of 1-10 GeV parameter to calculation and investigation spectrum of photon rate. We calculation and study the photon rate produced through bremsstrahlung processes from the stable QGP matter. The photon rate production from cg → dgy systems at bremsstrahlung processes are found to be increased with increased fugacity, decreased strength coupling, decreased the photons energy and temperature of system. The photons rate in cg → dgy is inc

The charge transfer at C23H17F8N8O2PRu, C44H30BF4N5O4Ru, C56H52CL5N5OOsP2 and C76H88F80N24O11P10Ru4 nitrosyl complexes are investigation and studies theoretically using the quantum consideration. Charge transfer behavior largely rely to the electric properties of nitrosyl complexes system whose depending on the main important parameters for the transmission rate constant such that: orientation transition energy, overlapping coupling coefficient, driving force energy, height barrier and Temperature T (K). Data results have been evaluated using a MATLAB program. Results show that rate of charge transfer increases due to increases the orientation transition energy.

   This research  studyies  wear  rate  of  composite  materials  by using Epoxy Resin and Polyurethane Rubber as a matrix  of weigt percentage (90:10) (Ep/Pu) and reinforced by PVC fibers and Aluminum fibers two dimension knitted mat with fractional volume(15 %), in different conditions like: lab conditions and after submerge the samples in water for different periods of time. . four kinds of materials were prepared: (Ep+pu), (Ep+Pu+PVC), (Ep+Pu+Al.F), (Ep+Pu+PVC+Al. F) .And the results have shown that the best wear resistance are for the hybrid composite material    (Ep + Pu+ PVC + Al. F) and wear rate of  all samples increased when it was submerged in water

This paper develops a fuzzy multi-objective model for solving aggregate production planning problems that contain multiple products and multiple periods in uncertain environments. We seek to minimize total production cost and total labor cost. We adopted a new method that utilizes a Zimmermans approach to determine the tolerance and aspiration levels. The actual performance of an industrial company was used to prove the feasibility of the proposed model. The proposed model shows that the method is useful, generalizable, and can be applied to APP problems with other parameters.