In this paper Volterra Runge-Kutta methods which include: method of order two and four will be applied to general nonlinear Volterra integral equations of the second kind. Moreover we study the convergent of the algorithms of Volterra Runge-Kutta methods. Finally, programs for each method are written in MATLAB language and a comparison between the two types has been made depending on the least square errors.
Sol-gel method was use to prepare Ag-SiO2 nanoparticles. Crystal structure of the nanocomposite was investigated by means of X-ray diffraction patterns while the color intensity was evaluated by spectrophotometry. The morphology analysis using atomic force microscopy showed that the average grain sizes were in range (68.96-75.81 nm) for all samples. The characterization of Ag-SiO2 nanoparticles were investigated by using Scanning Electron Microscopy (SEM). Ag-SiO2 NPs are highly stable and have significant effect on both Gram positive and negative bacteria. Antibacterial properties of the nanocomposite were tested with the use of Staphylococcus aureus (S. aureus) and Escherichia coli (E. coli) bacteria. The results have shown antibacteri
... Show MoreWith the increasing use of antibiotics around the world, the study and appreciation of antibiotics has become essential. An antibiotic formulation may include one or added active ingredients depending on the type and method of manufacturing the antibiotic. Antibiotics can only combat diseases of bacterial origin. As for viral diseases such as the common cold and influenza, antibiotics will not be able to combat them. The objective of this review is to digest the literature related to estimation of antibiotics and to show the methods that have been used in the estimation of the antibiotics (amoxicillin, ampicillin, cephalothin, carbenicillin, and cefotaxime) in medicinal preparations and a biological fluid for example blood
... Show MoreThe aim of this paper, is to study different iteration algorithms types two steps called, modified SP, Ishikawa, Picard-S iteration and M-iteration, which is faster than of others by using like contraction mappings. On the other hand, the M-iteration is better than of modified SP, Ishikawa and Picard-S iterations. Also, we support our analytic proof with a numerical example.
The aim of this paper is to introduce the concepts of asymptotically p-contractive and asymptotically severe accretive mappings. Also, we give an iterative methods (two step-three step) for finite family of asymptotically p-contractive and asymptotically severe accretive mappings to solve types of equations.
In this paper, we have been used the Hermite interpolation method to solve second order regular boundary value problems for singular ordinary differential equations. The suggest method applied after divided the domain into many subdomains then used Hermite interpolation on each subdomain, the solution of the equation is equal to summation of the solution in each subdomain. Finally, we gave many examples to illustrate the suggested method and its efficiency.
A new panel method had been developed to account for unsteady nonlinear subsonic flow. Two boundary conditions were used to solve the potential flow about complex configurations of airplanes. Dirichlet boundary condition and Neumann formulation are frequently applied to the configurations that have thick and thin surfaces respectively. Mixed boundary conditions were used in the present work to simulate the connection between thick fuselage and thin wing surfaces. The matrix of linear equations was solved every time step in a marching technique with Kelvin's theorem for the unsteady wake modeling. To make the method closer to the experimental data, a Nonlinear stripe theory which is based on a two-dimensional viscous-inviscid interac
... Show MoreLinear and nonlinear optical properties of epoxy/ Al2O3 nanocomposites system were studied for epoxy neat and (0.5, 1.5, 3, and 5) % Al2O3 nanocomposites.The band gap of epoxy and its nanocomposites was obtained at these weight ratios. Nonlinear optical properties experiments were performed using Q-switched Nd:YAG laser z-scan system.These experiments were carried out for different parameters: wavelengths (1064 nm and 532 nm), laser intensities (0.530, 0.679, and 0.772) GW/cm2 and weight ratio of Al2O3 nanocomposites. The results showed that the band gaps were decreased with increasing the weight ratio of nanoalumina except at 5wt% and the nonlinear refractive index coefficient is directly proportional to the incident intensities while o
... Show MoreThis study relates to the estimation of a simultaneous equations system for the Tobit model where the dependent variables ( ) are limited, and this will affect the method to choose the good estimator. So, we will use new estimations methods different from the classical methods, which if used in such a case, will produce biased and inconsistent estimators which is (Nelson-Olson) method and Two- Stage limited dependent variables(2SLDV) method to get of estimators that hold characteristics the good estimator .
That is , parameters will be estim
... Show MoreNonlinear diffraction patterns can be obtained by focusing a laser beam through a thin slice of the material. Here, we investigated experimentally the formation of the far field nonlinear diffraction patterns of cw laser beam at 532 nm passing through a quartz cuvette containing multi-wall carbon nanotubes (MWCNT's) suspended in acetone and in DI water at concentrations of 0.030.wt.%, 0.045 wt.%, 0.060 wt.%, and 0.075 wt.%. Our results show that increasing the concentration of both types of suspensions (MWCNTs in acetone and MWCNTs DI water) led to increase in the number of pattern rings which indicates an increase in their nonlinear refractive indices. Moreover, MWCNTs DI water suspension at a concentration of 0.075 wt. % was more effic
... Show MoreOscillation criterion is investigated for all solutions of the first-order linear neutral differential equations with positive and negative coefficients. Some sufficient conditions are established so that every solution of eq.(1.1) oscillate. Generalizing of some results in [4] and [5] are given. Examples are given to illustrated our main results.