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.

This research aims to numerically solve a nonlinear initial value problem presented as a system of ordinary differential equations. Our focus is on epidemiological systems in particular. The accurate numerical method that is the Runge-Kutta method of order four has been used to solve this problem that is represented in the epidemic model. The COVID-19 mathematical epidemic model in Iraq from 2020 to the next years is the application under study. Finally, the results obtained for the COVID-19 model have been discussed tabular and graphically. The spread of the COVID-19 pandemic can be observed via the behavior of the different stages of the model that approximates the behavior of actual the COVID-19 epidemic in Iraq. In our study, the COV

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.

To develop a petrol engine so that it works under the bi-engine pattern (producer gas-petrol) without any additional engine modifications, a single-point injection method inside the intake manifold is a simple and inexpensive method. Still, it leads to poor mixing performance between the air and producer gas. This deficiency can cause unsatisfactory engine performance and high exhaust emissions. In order to improve the mixing inside the intake manifold, nine separate cases were modelled to evaluate the impact of the position and angle orientation inside the intake manifold on the uniformity and spread of the mixture under AFR=2.07. A petrol engine (1.6 L), the maximum engine speed (8000 rpm), and bi-engine mode (petrol-producer ga

Numerical study of separation control on symmetrical airfoil, four digits (NACA

0012) by using rotating cylinder with double steps on its upper surface based on the computation of Reynolds-average Navier- Stokes equations was carried out to find the optimum configuration of unconventional airfoil for best aerodynamics performance. A model based on collocated Finite Volume Method was developed to solve the governing equations on a body-fitted coordinate system. A revised (k-w) model was proposed as a known turbulence model. This model was adapted to simulate the control effects of rotating cylinder. Numerical solutions were performed for flow around unconventional airfoil with cylinder to main stream velocities ratio in the range

This study is to investigate the possibility of using activated carbon prepared from Iraqi date-pits (ADP) which are produced from palm trees (Phoenix dactylifera L.) as low-cost reactive material in the permeable reactive barrier (PRB) for treating lead (Pb⁺²) from the contaminated groundwater, and then compare the results experimentally with other common reactive materials such as commercial activated carbon (CAC), zeolite pellets (ZP). Factors influencing sorption such as contact time, initial pH of the solution, sorbent dosage, agitation speed, and initial lead concentration has been studied. Two isotherm models were used for the description of sorption data (Langmuir and Freundlich). The maximum lead sorp

The present study was conducted to evaluate the effect of fungi Gigaspora margarita and Glomus desriticola in stimulating the resistance of the capsicum annuum L. towards the chromium and lead after 60 days, planting and using the pots in the glass house. The highest concentration of chromium and lead in the root was found in the presence of the mycorrhizal mixture (194.93, 150.40) μg / g, respectively, compared to the lowest concentration (90.69, 79.37) μg / g respectively, while the highest concentration of chromium and lead in the shoot was found in the presence of the mycorrhizal mixture (94.63, 79.33) μg / g respectively, compared with the lowest concentration in the control treatment (72.58, 60.70) μg / g respectively. The results