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.

This study includes the preparation of the ferrite nano ferrite Cu_xAl_0.3-XNi_0.7Fe₂O₄ (where: x = 0, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3) M using the auto combustion method (sol-gel), and citric acid was used as fuel for auto combustion. The ferrite samples were checked by X-ray diffraction (XRD), Field Emission Scanning Electron Microscopes (FE-SEM), and energy dispersive X-ray analyzer (EDX). They showed that the prepared compound has a face-centered cubic structure (FCC). The lattice constant increases with an increase in the percentage of doping of the copper ions, and a decrease for the aluminum ion and that the compound is porous and its grains are spherical, and there are no other

In this paper, a new technique is offered for solving three types of linear integral equations of the 2^nd kind including Volterra-Fredholm integral equations (LVFIE) (as a general case), Volterra integral equations (LVIE) and Fredholm integral equations (LFIE) (as special cases). The new technique depends on approximating the solution to a polynomial of degree  and therefore reducing the problem to a linear programming problem(LPP), which will be solved to find the approximate solution of LVFIE. Moreover, quadrature methods including trapezoidal rule (TR), Simpson 1/3 rule (SR), Boole rule (BR), and Romberg integration formula (RI) are used to approximate the integrals that exist in LVFIE. Also, a comparison between those

The present study aimed to identify the exact location and its relation to cognitive
method (risk_caution) to university students. The sample consisted of (300) students who
were chosen randomly and equally. The study results indicated that students possess an
internal exact location and they also use risk cognitive method. The study also indicated that
there is a prophesies which is an exact location for others to reach to caution cognitive
method. Depending on these results, the study recommended to benefit from the results of the
study variables and from the measurement of the exact location and method of cognitive
(risk_caution) to identify male and female students and especially by consulting units at
college

In an attempt to disposal from nuclear waste which threats our health and environments. Therefore we have to find appropriate method to immobilize nuclear waste. So, in this research the nuclear waste (Strontium hydroxide) was immobilized by Carbon nanotubes (CNTs).  The Nd-YAG laser with wave length 1064 nm, energy 750 mJ and 100 pulses used to prepare CNTs. After that adding Sr(HO)₂ powder to the CNTs colloidal in calculated rate to get homogenous mixing of CNTs-Sr(OH)_2. The Sr(HO)₂ absorbs carbon dioxide from the air to form strontium carbonate so, the  new solution is CNTs-SrCO₃. To dry solution putting three drops from the new solution on the glass slides. To investigate the radi

Darcy-Weisbach (D-W) is a typical resistance equation in pressured flow; however, some academics and engineers prefer Hazen-Williams (H-W) for assessing water distribution networks. The main difference is that the (D-W) friction factor changes with the Reynolds number, while the (H-W) coefficient is a constant value for a certain material. This study uses WaterGEMS CONNECT Edition update 1 to find an empirical relation between the (H-W) and (H-W) equations for two 400 mm and 500 mm pipe systems. The hydraulic model was done, and two scenarios were applied by changing the (H-W) coefficient to show the difference in results of head loss. The results showed a strong relationship between both equations with correlation coefficients of 0.999,

Research seeks to test the impact of the dimensions of mindfulness on  organizational Innovation, proposed in the light of the review literature on two variables of the research, which referred in General to the dynamic relationship between them, as result of weakness of mindfulness as one important factor driving the diversity of innovation and time, ways to sustain and preserve and then support innovations made by creators, weakness in the overall level of organizational Innovation, this represents the problem research, data collection over designing   identification, distributed to sample Formed from (30) head Department at a number of colleges of the University of Baghdad, results confirms the validity of resea

This paper is concerned with studying the numerical solution for the discrete classical optimal control problem (NSDCOCP) governed by a variable coefficients nonlinear hyperbolic boundary value problem (VCNLHBVP). The DSCOCP is solved by using the Galerkin finite element method (GFEM) for the space variable and implicit finite difference scheme (GFEM-IFDS) for the time variable to get the NS for the discrete weak form (DWF) and for the discrete adjoint weak form (DSAWF) While, the gradient projection method (GRPM), also called the gradient method (GRM), or the Frank Wolfe method (FRM) are used to minimize the discrete cost function (DCF) to find the DSCOC. Within these three methods, the Armijo step option (ARMSO) or the optimal step opt