A new efficient Two Derivative Runge-Kutta method (TDRK) of order five is developed for the numerical solution of the special first order ordinary differential equations (ODEs). The new method is derived using the property of First Same As Last (FSAL). We analyzed the stability of our method. The numerical results are presented to illustrate the efficiency of the new method in comparison with some well-known RK methods.

The main goal of this work is to obtain the plasma electron temperature Te by optical emission spectroscopy of low pressure microwave argon plasma, as a function of working pressure and microwave power. A plasma system was designed and constructed in our laboratory using a magnetron of domestic microwave oven with power 800W without any commercial part. The applied voltage on the magnetron electrical circuit is changed for the purpose of obtaining the variable values of the microwave power. The spectral detection is performed with a spectrometer of wavelength range (200−1000nm). The working pressure and magnetron applied voltage were 0.3-3.0mbar and 180-240V, respectively. Two methods had been applied to estimate the electron temperatu

     A partial temporary immunity SIR epidemic model involv nonlinear treatment rate is proposed and studied. The basic reproduction number  is determined. The local and global stability of all equilibria of the model are analyzed. The conditions for occurrence of local bifurcation in the proposed epidemic model are established. Finally, numerical simulation is used to confirm our obtained analytical results and specify the control set of parameters that affect the dynamics of the model.

ABSTRACT
                  The research aims to analyze the value chain of dairy products in Iraq (Abu Ghraib/Study Case) factories for the year 2022, where value chain rings are identified to discuss and track the most important determinants and problems in the value chain rings of dairy products and their basic and secondary activities, as well as calculate the value added of the products by subtracting the total revenues of products from their variable costs. Research data were collected for the period 2022. Preliminary information and data from its field sources and personal interviews were collected through a questionnaire prepa

In this research study failed Annunciation No. 10 for the fourth phase of the pressure of carbon dioxide of the company for Southern Fertilizers and repeated the failures more than once for the same gospel was a detailed study of the gospel included a series tests for properties Mechanical and Structural addition to the tests microscopic and scanning electron microscope shows m This study parameters and a failure Elal well as the existence of an old internal cracks in the metal of the Annunciation