In this paper, Touchard polynomials (TPs) are presented for solving Linear Volterra integral equations of the second kind (LVIEs-2k) and the first kind (LVIEs-1k) besides, the singular kernel type of this equation. Illustrative examples show the efficiency of the presented method, and the approximate numerical (AN) solutions are compared with one another method in some examples. All calculations and graphs are performed by program MATLAB2018b.

In this research, Haar wavelets method has been utilized to approximate a numerical solution for Linear state space systems. The solution technique is used Haar wavelet functions and Haar wavelet operational matrix with the operation to transform the state space system into a system of linear algebraic equations which can be resolved by MATLAB over an interval from 0 to . The exactness of the state variables can be enhanced by increasing the Haar wavelet resolution. The method has been applied for different examples and the simulation results have been illustrated in graphics and compared with the exact solution.

A new method based on the Touchard polynomials (TPs) was presented for the numerical solution of the linear Fredholm integro-differential equation (FIDE) of the first order and second kind with condition. The derivative and integration of the (TPs) were simply obtained. The convergence analysis of the presented method was given and the applicability was proved by some numerical examples. The results obtained in this method are compared with other known results.

Foundations supporting reciprocating engines, radar towers, turbines, large electric motors, and generators, etc. are subject to vibrations caused by unbalanced machine forces as well as the static weight of the machine. If these vibrations are excessive, they may damage the machine or cause it not to function properly. In the case of block foundation, if changes in size and mass of the foundation do not lead to a satisfactory design, a pile foundation may be used. In this study, the dynamic response of piles and pile Groups in dry sand is investigated experimentally. The analysis involves the displacement response under harmonic excitation. In addition, a numerical modeling by using finite element method with a three-dimensional formula

This paper introduces a non-conventional approach with multi-dimensional random sampling to solve a cocaine abuse model with statistical probability. The mean Latin hypercube finite difference (MLHFD) method is proposed for the first time via hybrid integration of the classical numerical finite difference (FD) formula with Latin hypercube sampling (LHS) technique to create a random distribution for the model parameters which are dependent on time t . The LHS technique gives advantage to MLHFD method to produce fast variation of the parameters’ values via number of multidimensional simulations (100, 1000 and 5000). The generated Latin hypercube sample which is random or non-deterministic in nature is further integrated with the FD method t

The present study deals with the effect of teaching oral Communication Strategies on English language learners. The use of oral communication strategies not only solves learners’ communication problems, but also enhances the learner’s interaction in target language, which in turn, improves their oral proficiency .The sample of this study is EFL students in the first stage at the Department of English Language, morning studies, College of Education /Ibn-Rushd .The sample of the study consists of (60) students distributed on experimental group(A) includes (30) students, and (30) students as control group(B). In order to achieve the aim of the study, and to gain a closer idea about the impact of teaching oral Communication Strategies on th

This research aimed to predict the permanent deformation (rutting) in conventional and rubberized asphalt mixes under repeated load conditions using the Finite Element Method (FEM). A three-dimensional (3D) model was developed to simulate the Wheel Track Testing (WTT) loading. The study was conducted using the Abaqus/Standard finite element software. The pavement slab was simulated using a nonlinear creep (time-hardening) model at 40°C. The responses of the viscoplastic model under the influence of the trapezoidal amplitude of moving wheel loadings were determined for different speeds and numbers of cycles. The results indicated that a wheel speed increase from 0.5Km/h to 1.0Km/h decreased the rut depth by about 22% and 24% in conv

Asmari is the main productive reservoir in Abu Ghirab oilfield in the south-east part of Iraq. It has history production extends from 1976 up to now with several close periods. Recently, the reservoir suffers some problems in production, which are abstracted as water production rising with oil production declining in most wells. The water problem type of the field and wells is identified by using Chan's diagnostic plots (water oil ratio (WOR) and derivative water oil ratio (WOR') against time). The analytical results show that water problem is caused by the channeling due to high permeability zones, high water saturation zones, and faults or fracturing. The numerical approach is also used to study the water movement inside the reser