The method of operational matrices based on different types of polynomials such as Bernstein, shifted Legendre and Bernoulli polynomials will be presented and implemented to solve the nonlinear Blasius equations approximately. The nonlinear differential equation will be converted into a system of nonlinear algebraic equations that can be solved using Mathematica®12. The efficiency of these methods has been studied by calculating the maximum error remainder ( ), and it was found that their efficiency increases as the polynomial degree (n) increases, since the errors decrease. Moreover, the approximate solutions obtained by the proposed methods are compared with the solution of the 4th order Runge-Kutta method (RK4), which gives very good agreement. In addition, the convergence of the proposed approximate methods is given based on one of the Banach fixed point theorem results.
In this paper, double Sumudu and double Elzaki transforms methods are used to compute the numerical solutions for some types of fractional order partial differential equations with constant coefficients and explaining the efficiently of the method by illustrating some numerical examples that are computed by using Mathcad 15.and graphic in Matlab R2015a.
Background: Unlike normal EEG patterns, the epileptiform abnormal pattern is characterized by different mor phologies such as the high-frequency oscillations (HFOs) of ripples on spikes, spikes and waves, continuous and sporadic spikes, and ploy2 spikes. Several studies have reported that HFOs can be novel biomarkers in human epilepsy study. S) Method: To regenerate and investigate these patterns, we have proposed three large scale brain network models (BNM by linking the neural mass model (NMM) of Stefanescu-Jirsa 2D (S-J 2D) with our own structural con nectivity derived from the realistic biological data, so called, large-scale connectivity connectome. These models include multiple network connectivity of brain regions at different
... Show MoreSolubility problem of many of effective pharmaceutical molecules are still one of the major obstacle in theformulation of such molecules. Candesartan cilexetil (CC) is angiotensin II receptor antagonist with very low water solubility and this result in low and variable bioavailability. Self- emulsifying drug delivery system (SEDDS) showed promising result in overcoming solubility problem of many drug molecules. CC was prepared as SEDDS by using novel combination of two surfactants (tween 80 and cremophore EL) and tetraglycol as cosurfactant, in addition to the use of triacetin as oil. Different tests were performed in order to confirm the stability of the final product which includes thermodynamic study, determination of self-emulsificat
... Show MoreParticulate matter (PM) emitted from diesel engine exhaust have been measured in terms of mass, using
99.98 % pure ethanol blended directly, without additives, with conventional diesel fuel (gas – oil),to
get 10 % , 15 %, 20 % ethanol emulsions . The resulting PM collected has been compared with those
from straight diesel. The engine used is a stationary single cylinder, variable compression ratio Ricardo
E6/US. This engine is fully instrumented and could run as a compression or spark ignition.
Observations showed that particulate matter (PM) emissions decrease with increasing oxygenate
content in the fuel, with some increase of fuel consumption, which is due to the lower heating value of
ethanol. The reduction in
The cost‐effective dual functions zeolite‐carbon composite (DFZCC) was prepared using an eco‐friendly substrate prepared from bio‐waste and an organic adhesive at intermediate conditions. The green synthesis method used in this study ensures that chemically harmless compounds are used to obtain a homogeneous distribution of zeolite over porous carbon. The greenly prepared dual‐function composite was extensively characterized using Fourier transform infrared, X‐ray diffraction, thermogravimetric analysis, N2 adsorption/desorption isotherms, field emission scanning electron microscope, dispersive analysis by X‐ray, and point of zero charges. DFZCC had a surface area o
The removal of commercial orange G dye from its aqueous solution by adsorption on tobacco leaves (TL) was studied in respect to different factor that affected the adsorption process. These factors including the tobacco leaves does, period of orange G adsorption, pH, and initial orange G dye concentration .Different types of isotherm models were used to describe the orange G dye adsorption onto the tobacco leaves. The experimental results were compared using Langmuir, and frundlich adsorption isotherm, the constants for these two isotherm models was determined. The results fitted frundlich model with value of correlation coefficient equal to (0.981). The capacity of adsorption for the orange G dye was carried out using various kinetic models
... Show MoreA 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 MoreElectromechanical actuators are used in a wide variety of aerospace applications such as missiles, aircrafts and spy-fly etc. In this work a linear and nonlinear fin actuator mathematical model has been developed and its response is investigated by developing an algorithm for the system using MATLAB. The algorithm used to the linear model is the state space algorithm while the algorithm used to the nonlinear model is the discrete algorithm. The huge moment constant is varied from (-3000 to 3000) and the damping ratio is varied from (0.4 to 0.8).
The comparison between linear and nonlinear fin actuator response results shows that for linear model, the maximum overshoot is about 10%,
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