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.

In this paper a modified approach have been used to find the approximate solution of ordinary delay differential equations with constant delay using the collocation method based on Bernstien polynomials.

In this paper, a new form of 2D-plane curves is produced and graphically studied. The name of my daughter "Noor" has been given to this curve; therefore, Noor term describes this curve whenever it is used in this paper. This curve is a form of these opened curves as it extends in the infinity along both sides from the origin point. The curve is designed by a circle/ ellipse which are drawing curvatures that tangent at the origin point, where its circumference is passed through the (0,2a). By sharing two vertical lined points of both the circle diameter and the major axis of the ellipse, the parametric equation is derived. In this paper, a set of various cases of Noor curve are graphically studied by two curvature cases;

A new, Simple, sensitive and accurate spectrophotometric methods have been developed for the determination of sulfamethoxazole (SMZ) drug in pure and dosage forms. This method based on the reaction of sulfamethoxazole (SMZ) with 1,2-napthoquinone-4-sulphonic acid (NQS) to form Nalkylamono naphthoquinone by replacement of the sulphonate group of the naphthoquinone sulphonic acid by an amino group. The colored chromogen shows absorption maximum at 460 nm. The optimum conditions of condensation reaction forms were investigated by (1) univariable method, by optimizing the effect of experimental variables (different bases, reagent concentration, borax concentration and reaction time), (2) central composite design (CCD) including the effect of

In this paper,the homtopy perturbation method (HPM) was applied to obtain the approximate solutions of the fractional order integro-differential equations . The fractional order derivatives and fractional order integral are described in the Caputo and Riemann-Liouville sense respectively. We can easily obtain the solution from convergent the infinite series of HPM . A theorem for convergence and error estimates of the HPM for solving fractional order integro-differential equations was given. Moreover, numerical results show that our theoretical analysis are accurate and the HPM can be considered as a powerful method for solving fractional order integro-diffrential equations.

Electrical Discharge Machining (EDM) is a widespread Nontraditional Machining (NTM) processes for manufacturing of a complicated geometry or very hard metals parts that are difficult to machine by traditional machining operations. Electrical discharge machining is a material removal (MR) process characterized by using electrical discharge erosion. This paper discusses the optimal parameters of EDM on high-speed steel (HSS) AISI M2 as a workpiece using copper and brass as an electrode. The input parameters used for experimental work are current (10, 24 and 42 A), pulse on time (100, 150 and 200 µs), and pulse off time (4, 12 and 25 µs) that have effect on the material removal rate (MRR), electrode wear rate (EWR) and wear ratio (WR). A

The major goal of this research was to use the Euler method to determine the best starting value for eccentricity. Various heights were chosen for satellites that were affected by atmospheric drag. It was explained how to turn the position and velocity components into orbital elements. Also, Euler integration method was explained. The results indicated that the drag is deviated the satellite trajectory from a keplerian orbit. As a result, the Keplerian orbital elements alter throughout time. Additionally, the current analysis showed that Euler method could only be used for low Earth orbits between (100 and 500) km and very small eccentricity (e = 0.001).

In this paper the nuclear structure of some of Si-isotopes namely, ^28,32,36,40Si have been studied by calculating the static ground state properties of these isotopes such as charge, proton, neutron and mass densities together with their associated rms radii, neutron skin thicknesses, binding energies, and charge form factors. In performing these investigations, the Skyrme-Hartree-Fock method has been used with different parameterizations; SkM*, S1, S3, SkM, and SkX. The effects of these different parameterizations on the above mentioned properties of the selected isotopes have also been studied so as to specify which of these parameterizations achieves the best agreement between calculated and experimental data. It can be ded

Background: The world is in front of two emerging problems being scarceness of virgin re-sources for bioactive materials and the gathering of waste production. Employment of the surplus waste in the mainstream production can resolve these problems. The current study aimed to prepare and characterize a natural composite CaO-SiO2 based bioactive material derived from naturally sustained raw materials. Then deposit this innovative novel bioactive coating composite materials overlying Yttria-stabilized tetragonal zirconia substrate. Mate-rials and method; Hen eggshell-derived calcium carbonate and rice husk-derived silica were extracted from natural resources to prepare the composite coating material. The manufac-tured powder was characterized