In this paper, the computational method (CM) based on the standard polynomials has been implemented to solve some nonlinear differential equations arising in engineering and applied sciences. Moreover, novel computational methods have been developed in this study by orthogonal base functions, namely Hermite, Legendre, and Bernstein polynomials. The nonlinear problem is successfully converted into a nonlinear algebraic system of equations, which are then solved by Mathematica®12. The developed computational methods (D-CMs) have been applied to solve three applications involving well-known nonlinear problems: the Darcy-Brinkman-Forchheimer equation, the Blasius equation, and the Falkner-Skan equation, and a comparison between the met

The aim of this study is to identify the effect of particle size and to increase the concentration of Iraqi bentonite on rheological properties in order to evaluate its performance and to know if it can be used as drilling fluid without additives or not. In this study, Iraqi bentonite was carried out by mineral composition (XRD), chemical composition (XRF) and Particle size distribution (PSD), and its rheological properties were measured at different particle size and concentration. The results showed that when the particle size of Iraqi bentonite decreased, and the rheological properties were increased with increased concentration of Iraqi bentonite. Also, Iraqi bentonite was unable to use as drilling fluid without certain additives.

The paper is concerned with the state and proof of the existence theorem of a unique solution (state vector) of couple nonlinear hyperbolic equations (CNLHEQS) via the Galerkin method (GM) with the Aubin theorem. When the continuous classical boundary control vector (CCBCV) is known, the theorem of existence a CCBOCV with equality and inequality state vector constraints (EIESVC) is stated and proved, the existence theorem of a unique solution of the adjoint couple equations (ADCEQS) associated with the state equations is studied. The Frcéhet derivative derivation of the "Hamiltonian" is obtained. Finally the necessary theorem (necessary conditions "NCs") and the sufficient theorem (sufficient conditions" SCs") for optimality of the stat

In this paper, we established a mathematical model of an SI1I2R epidemic disease with saturated incidence and general recovery functions of the first disease I1. Considering the basic reproduction number, we obtained conditions for both disease-free and co-existing cases. The equilibrium points local stability is verified by using the Routh-Hurwitz criterion, while for the global stability, we used a suitable Lyapunov function to analyze the endemic spread of the positive equilibrium point. Moreover, we carried out the local bifurcation around both equilibrium points (disease-free and co-existing), where we obtained that the disease-free equilibrium point undergoes a transcritical bifurcation. We conduct numerical simulations that suppo

In this study, SnO2 nanoparticles were prepared from cost-low tin chloride (SnCl2.2H2O) and ethanol by adding ammonia solution by the sol-gel method, which is one of the lowest-cost and simplest techniques. The SnO2 nanoparticles were dried in a drying oven at a temperature of 70°C for 7 hours. After that, it burned in an oven at a temperature of 200°C for 24 hours. The structure, material, morphological, and optical properties of the synthesized SnO2 in nanoparticle sizes are studied utilizing X-ray diffraction. The Scherrer expression was used to compute nanoparticle sizes according to X-ray diffraction, and the results needed to be scrutinized more closely. The micro-strain indicates the broadening of diffraction peaks for nano

In this work Laser wireless video communication system using intensity modualtion direct
detection IM/DD over a 1 km range between transmitter and receiver is experimentally investigated and
demonstrated. Beam expander and beam collimeter were implemented to collimete laser beam at the
transmitter and focus this beam at the receiver respectively. The results show that IM/DD communication
sysatem using laser diode is quite attractive for transmitting video signal. In this work signal to noise
ratio (S/N) higher than 20 dB is achieved in this work.

Many of the dynamic processes in different sciences are described by models of differential equations. These models explain the change in the behavior of the studied process over time by linking the behavior of the process under study with its derivatives. These models often contain constant and time-varying parameters that vary according to the nature of the process under study in this We will estimate the constant and time-varying parameters in a sequential method in several stages. In the first stage, the state variables and their derivatives are estimated in the method of penalized splines(p- splines) . In the second stage we use pseudo lest square to estimate constant parameters, For the third stage, the rem

In this study, the results of x-ray diffraction methods were used to determine the Crystallite size and Lattice strain of Cu2O nanoparticles then to compare the results obtained by using variance analysis method, Scherrer method and Williamson-Hall method. The results of these methods of the same powder which is cuprous oxide, using equations during the determination the crystallite size and lattice strain, It was found that the results obtained the values of the crystallite size (28.302nm) and the lattice strain (0.03541) of the variance analysis method respectively and for the Williamson-Hall method were the results of the crystallite size (21.678nm) and lattice strain (0.00317) respectively, and Scherrer method which gives the value of c