The main work of this paper is devoted to a new technique of constructing approximated solutions for linear delay differential equations using the basis functions power series functions with the aid of Weighted residual methods (collocations method, Galerkin’s method and least square method).

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.

Market share is a major indication of business success. Understanding the impact of numerous economic factors on market share is critical to a company’s success. In this study, we examine the market shares of two manufacturers in a duopoly economy and present an optimal pricing approach for increasing a company’s market share. We create two numerical models based on ordinary differential equations to investigate market success. The first model takes into account quantity demand and investment in R&D, whereas the second model investigates a more realistic relationship between quantity demand and pricing.

The research aims to find approximate solutions for two dimensions Fredholm linear integral equation. Using the two-variables of the Bernstein polynomials we find a solution to the approximate linear integral equation of the type two dimensions. Two examples have been discussed in detail.

The researcher concluded that it consists of several types of structures, where the intellectual structure related to the choice of the idea, its treatment, its effect, the choice of the topic, the way ideas are addressed and presented in the film, and then the dramatic structure of the film's characters, the formulation of its events, its dramatic composition, its temporal arrangement, the identification of the parties to the conflict and their management, then these are formulated. Visions and ideas through the visual and audio signal systems, which work to highlight the stylistic features in the character of the film director.

The construction industry in Iraq suffers from many problems, perhaps the most important of which is the delay in time and the increase in costs. Therefore, it was necessary to try to adopt a new methodology that would help in overcoming these problems. It was suggested to combine building information modeling with the agile management approach because this technique and methodology is modern and helps in reducing time and cost and improving quality. This paper aims to know the status of using Building Information Modeling (BIM) and Agile Project management (APM) in Iraq and to shed light on the merging of this integration, explaining the benefits, difficulties, and workflow practices, finding the most influencing factors on the tim

We present a reliable algorithm for solving, homogeneous or inhomogeneous, nonlinear ordinary delay differential equations with initial conditions. The form of the solution is calculated as a series with easily computable components. Four examples are considered for the numerical illustrations of this method. The results reveal that the semi analytic iterative method (SAIM) is very effective, simple and very close to the exact solution demonstrate reliability and efficiency of this method for such problems.