The Wang-Ball polynomials operational matrices of the derivatives are used in this study to solve singular perturbed second-order differential equations (SPSODEs) with boundary conditions. Using the matrix of Wang-Ball polynomials, the main singular perturbation problem is converted into linear algebraic equation systems. The coefficients of the required approximate solution are obtained from the solution of this system. The residual correction approach was also used to improve an error, and the results were compared to other reported numerical methods. Several examples are used to illustrate both the reliability and usefulness of the Wang-Ball operational matrices. The Wang Ball approach has the ability to improve the outcomes by minimi

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.

A mathematical model constructed to study the combined effects of the concentration and the thermodiffusion on the nanoparticles of a Jeffrey fluid with a magnetic field effect the process of containing waves in a three-dimensional rectangular porous medium canal. Using the HPM to solve the nonlinear and coupled partial differential equations. Numerical results were obtained for temperature distribution, nanoparticles concentration, velocity, pressure rise, pressure gradient, friction force and stream function. Through the graphs, it was found that the velocity of fluid rises with the increase of a mean rate of volume flow and a magnetic parameter, while the velocity goes down with the increasing a Darcy number and lateral walls. Also, t

The general objective of the research is to better understand changes in land cover and their impact on climatic factors by measuring changes in land cover for the Baghdad city for the period 1999-2021 and evaluating changes in land cover and measuring changes in climatic factors (relative humidity and evaporation). This study from 1999 to 2021 and in two different seasons: the April of the growing season and August the dry season. When using the supervised classification method to determine the differences, the results showed remarkable changes, the study showed the spatial variations in LC from 1999 to 2021 as follows: increase in the vegetation and water bodies during April and decrease this in August while the soil and built up decreas

A field experiment was carried out in Horticulture Department / Collage of Agricultur e/University of Baghdad to study influence of adding ascorbic acid(asa) and bread yeast extract in snap bean cv.primel under irrigation with saline water using sodium chloride salt (NaCl) during spr ing season of 2016 .A factorial experiment using Randomized Complete Block Design( RCBD) with three replications wereconducted . The first factor includes three treatments of salinity which were tap water ( S0), 4ds.m-1(S1) and 8ds.m-1 (S2) . The second factor includes three treatments which were control treatment without any adding (C) ,ascorbic acid 0.3g.l-1( A ) and yeast extract 12g.l -1( Y ). Results showed significant and gradually decreases in all studie

Contemporary residential neighborhoods suffer from weak sustainability of urban residential environments as a result of the adoption of inefficient spatial organization at the neighborhood unit level. This resulted negative characteristics which affected the achievement of sustainable development plans for the residential environment that constitute the majority of the urban fabric of cities.

The physical affordances ,within the vocabulary of recent times,overcame the spiritual ones and affected the residential environment. Accordingly,the concept of space changed in contemporary residential areas through the dominance of the physical aspect (mass) on the symbolic aspect (space).The modern technology occupied an important level b

The purpose of this research is to highlight the relationship between the   administrative investigation and the improvement of institutional performance, and the research sought to achieve a set of cognitive and applied goals. the administrative investigation is the modern trend of managing the offices of the general  hginspectors and the main source to build the necessary standards to manage and invest its resources efficiently and effectively required to achieve the goals it seeks. The institutional performance is the cornerstone for the implementation of all tasks and duties carried out by institutions operating within the borders of a particular country, The significant change