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.
N, N′- bis[4-hydroxy phenyl] pyromillitdiimide [II] was prepared from the corresponding diamic acid , which was transfered to its new ester by the reaction with chloroethyl acetate [III ], [III] was used to prepare the novel hydrazide derivative [IV] , which was allowed to react with several aldehydes to yield the hydrazones [V – IX]. All the new compounds were synthesized , and characterized by their melting points .HNMR for some of them1FTIR,C,H,N analysis and ,
N, N′- bis[4-hydroxy phenyl] pyromillitdiimide [II] was prepared from the corresponding diamic acid , which was transfered to its new ester by the reaction with chloroethyl acetate [III ], [III] was used to prepare the novel hydrazide derivative [IV] , which was allowed to react with several aldehydes to yield the hydrazones [V – IX]. All the new compounds were synthesized , and characterized by their melting points .HNMR for some of them1FTIR,C,H,N analysis and ,
Abstract
This work involves the manufacturing of MAX phase materials include V2AlC and Cr2AlC using powder metallurgy as a new class of materials which characterized by regular crystals in lattice. Corrosion behavior of these materials was investigated by Potentiostat to estimate corrosion resistance and compared with the most resistant material represented by SS 316L. The experiments were carried out in 0.01N of NaOH solution at four temperatures in the range of 30–60oC. Polarization resistance values which calculated by Stern-Geary equation indicated that the MAX phase materials more resistant than SS 316L. Also cyclic polarization tests confirme
... Show MoreThe tight gas is one of the main types of the unconventional gas. Typically the tight gas reservoirs consist of highly heterogeneous low permeability reservoir. The economic evaluation for the production from tight gas production is very challenging task because of prevailing uncertainties associated with key reservoir properties, such as porosity, permeability as well as drainage boundary. However one of the important parameters requiring in this economic evaluation is the equivalent drainage area of the well, which relates the actual volume of fluids (e.g gas) produced or withdrawn from the reservoir at a certain moment that changes with time. It is difficult to predict this equival
A new imidazolidine 4-one derivative, of namly 2-[2-(4-Bromo-phenyl)-imidazo [1,2-a] pyridine-3-yl]-3-(4-nitro-phenyl)-imidazolidine-4-one (BPIPNP) was investigated as corrosion inhibitor for carbon steel in salty (3.5% NaCl) and acidic (0.5M HCl) solutions using potentiometric polarization measurements. The results revealed that the percentage inhibition efficiencies (%IE) in the salty solution (90.67%) are greater than that in the acidic solution (83.52%). Experimentally, the thermodynamic parameters obtained have supported a physical adsorption mechanism and which followed Langmuir adsorption isotherm. Density Functional Theory (DFT) of quantum mechanical method with B3LYP 6-311++G (2d, 2p) level was used to calculate geometrical stru
... Show MoreThe aim of this article is to solve the Volterra-Fredholm integro-differential equations of fractional order numerically by using the shifted Jacobi polynomial collocation method. The Jacobi polynomial and collocation method properties are presented. This technique is used to convert the problem into the solution of linear algebraic equations. The fractional derivatives are considered in the Caputo sense. Numerical examples are given to show the accuracy and reliability of the proposed technique.
High-intensity laser-produced plasma has been extensively investigated in many studies. In this demonstration, a new spectral range was observed in the resulted spectra from the laser-plasma interaction, which opens up new discussions for new light source generation. Moreover, the characterizations of plasma have been improved through the interaction process of laser-plasma. Three types of laser were incorporated in the measurements, continuous-wave CW He-Ne laser, CW diode green laser, pulse Nd: YAG laser. As the plasma system, DC glow discharge plasma under the vacuum chamber was considered in this research. The plasma spectral peaks were evaluated, where they refer to Nitrogen gas. The results indicated that the
... Show MoreIn this paper, we introduce and discuss an algorithm for the numerical solution of two- dimensional fractional partial differential equation with parameter. The algorithm for the numerical solution of this equation is based on implicit and an explicit difference method. Finally, numerical example is provided to illustrate that the numerical method for solving this equation is an effective solution method.