The time fractional order differential equations are fundamental tools that are used for modeling neuronal dynamics. These equations are obtained by substituting the time derivative of order where , in the standard equation with the Caputo fractional formula. In this paper, two implicit difference schemes: the linearly Euler implicit and the Crank-Nicolson (CN) finite difference schemes, are employed in solving a one-dimensional time-fractional semilinear equation with Dirichlet boundary conditions. Moreover, the consistency, stability and convergence of the proposed schemes are investigated. We prove that the IEM is unconditionally stable, while CNM is conditionally stable. Furthermore, a comparative study between these two schemes will be conducted via numerical experiments. The efficiency of the proposed schemes in terms of absolute errors, order of accuracy and computing time will be reported and discussed.
Graphene-carbon nitride can be synthesized from thiourea in a single step at a temperature of four hours at a rate of 2.3 ℃/min. Graphene-carbon nitride was characterized by Fourier-transform infrared spectroscopy (FTIR), energy dispersive X-ray analysis (EDX), scanning electron microscopy, and spectrophotometry (UV-VIS). Graphene-carbon nitride was found to consist of triazine and heptazine structures, carbon, and nitrogen. The weight percentage of carbon and the atomic percentage of carbon are 40.08%, and the weight percentage of nitrogen and the atomic percentage of nitrogen are 40.08%. Therefore, the ratio and the dimensions of the graphene-carbon nitride were characterized by scanning electron microscopy, and it was found that the
... Show MoreCoaxial (wire-cylinder) electrodes arrangements are widely used for electrostatic deposition of dust particles in flue gases, when a high voltage is applied to electrodes immersed in air and provide a strongly non-uniform electric field. The efficiency of electrostatic filters mainly depends on the value of the applied voltage and the distribution of the electric field. In this work, a two-dimensional computer simulation was constructed to study the effect of different applied voltages (20, 22, 25, 26, 28, 30 kV) on the inner electrode and their effect on the efficiency of the electrostatic precipitator. Finite Element Method (FEM) and COMSOL Multiphysics software were used to simulate the cross section of a wire cylinder. The results sh
... Show MoreThis paper presents a computer simulation model of a thermally activated roof (TAR) to cool a room using cool water from a wet cooling tower. Modeling was achieved using a simplified 1-D resistance-capacitance thermal network (RC model) for an infinite slab. Heat transfer from the cooling pipe network was treated as 2-D heat flow. Only a limited number of nodes were required to obtain reliable results. The use of 6th order RC-thermal model produced a set of ordinary differential equations that were solved using MATLAB - R2012a. The computer program was written to cover all possible initial conditions, material properties, TAR system geometry and hourly solar radiation. The cool water supply was considered time
... Show MoreBack ground: During acrylic resin processing, the mold must be separated from the surface of the gypsum to prevent liquid resin from penetrating into the gypsum, and water from the gypsum seeping into the acrylic resin. For many years, tin foil was the most acceptable separating medium, and because it's difficult to apply, a tin-foil substitute is used. In this study, olive oil is used as an alternative to tin foil separating medium for first time, so the aim of the study was to evaluate its effect as a separating medium on some physical properties such as (surface roughness, water sorption and solubility) of acrylic resins denture base comparing it with those processed using tin-foil and tin foil substitute such as (cold mold seal) separat
... Show MoreIn this work, a class of stochastically perturbed differential systems with standard Brownian motion of ordinary unperturbed differential system is considered and studied. The necessary conditions for the existence of a unique solution of the stochastic perturbed semi-linear system of differential equations are suggested and supported by concluding remarks. Some theoretical results concerning the mean square exponential stability of the nominal unperturbed deterministic differential system and its equivalent stochastically perturbed system with the deterministic and stochastic process as a random noise have been stated and proved. The proofs of the obtained results are based on using the stochastic quadratic Lyapunov function meth
... Show MoreThis paper presents a three-dimensional Dynamic analysis of a rockfill dam with different foundation depths by considering the dam connection with both the reservoir bed and water. ANSYS was used to develop the three-dimensional Finite Element (FE) model of the rockfill dam. The essential objective of this study is the discussion of the effects of different foundation depths on the Dynamic behaviour of an embanked dam. Four foundation depths were investigated. They are the dam without foundation (fixed base), and three different depths of the foundation. Taking into consideration the changing of upstream water level, the empty, minimum, and maximum water levels, the results of the three-dimensional F
Due to the lack of statistical researches in studying with existing (p) of Exogenous Input variables, and there contributed in time series phenomenon as a cause, yielding (q) of Output variables as a result in time series field, to form conceptual idea similar to the Classical Linear Regression that studies the relationship between dependent variable with explanatory variables. So highlight the importance of providing such research to a full analysis of this kind of phenomena important in consumer price inflation in Iraq. Were taken several variables influence and with a direct connection to the phenomenon and analyzed after treating the problem of outliers existence in the observations by (EM) approach, and expand the sample size (n=36) to
... Show Morepriorities of materials research due to their promising properties, especially in the field of thermoelectricity. The efficiency or performance of thermoelectric devices is expressed in terms of the thermoelectric figure-of-merit (ZT) – a standard indicator of a material’s thermoelectric properties for use in cooling systems. The evaluation of ZT is principally determined by the thermoelectric characteristics of the nanomaterials. In this paper, a set of investigative computations was performed to study the thermoelectric properties of monolayer TMDCs according to the semiclassical treatment of the Boltzmann transport equation. It was confirmed that the thermoelectric properties of 2D materials can be greatly improved compared with thei
... Show MoreIn this paper, a new technique is offered for solving three types of linear integral equations of the 2nd kind including Volterra-Fredholm integral equations (LVFIE) (as a general case), Volterra integral equations (LVIE) and Fredholm integral equations (LFIE) (as special cases). The new technique depends on approximating the solution to a polynomial of degree and therefore reducing the problem to a linear programming problem(LPP), which will be solved to find the approximate solution of LVFIE. Moreover, quadrature methods including trapezoidal rule (TR), Simpson 1/3 rule (SR), Boole rule (BR), and Romberg integration formula (RI) are used to approximate the integrals that exist in LVFIE. Also, a comparison between those
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