In this paper Volterra Runge-Kutta methods which include: method of order two and four will be applied to general nonlinear Volterra integral equations of the second kind. Moreover we study the convergent of the algorithms of Volterra Runge-Kutta methods. Finally, programs for each method are written in MATLAB language and a comparison between the two types has been made depending on the least square errors.

Abstract:                                        

   We can notice cluster data in social, health and behavioral sciences, so this type of data have a link between its observations and we can express these clusters through the relationship between measurements on units within the same group.

    In this research, I estimate the reliability function of cluster function by using the seemingly unrelate

Companies need to educate people about the facts that characterize the business. This is the mission of promotion, it is an important marketing activity, promotion communicates with others and seeks to provide customers with a new business process experience.
Advertising is the most important methods of promotion and the best way to reach an audience. Once the organization advertises its products and services, it can operate in a competitive environment. Marketing competition requires knowledge of humanity that must be affected and convinced. Advertising should create Desires and need for satisfaction. This research comes in the study of visual representations of this psychological incident and how to use it communicatively to create

    The current study performed in order to detect and quantify epicatechin in two tea samples of Camellia sinensis (black and green tea) by thin layer chromatography (TLC) and high performance liquid chromatography (HPLC). Extraction of epicatechin from black and green tea was done by using two different methods: maceration (cold extraction method) and decoction (hot extraction method) involved using three different solvents which are  absolute ethanol, 50% aqueous ethanol and water  for both extraction methods using room temperature and direct heat respectively. Crude extracts of two tea samples that obtained from two methods were fractionated by using two solvents with different polarity (chloroform and

Type-1 diabetes is defined as destruction of pancreatic beta cell, virus and bacteria are some environmental factor for this disease. The study included 25 patients with type-1 diabetes mellitus aged between 8 – 25 years from Baghdad hospital and 20 healthy persons as control group. Anti-rubella IgG and IgM, anti-Chlamydia pneumonia IgG and IgM were measured by ELISA technique while anti-CMV antibody were measured by immunofluorescence technique. The aim of current study was to know the trigger factor for type-1 diabetes. There were significant differences (P<0.05) between studied groups according to parameters and the results lead to suggest that Chlamydia pneumonia, CMV and rubella virus may trigger type-1 diabetes mellitus in Iraqi pat

Background: Periodontitis is an inflammatory disease that affects the supporting tissues of the teeth; Smoking is an important risk factor for periodontitis induces alveolar bone loss and cause an imbalance between bone resorption and bone deposition. The purpose of this study is to detect and compare the presence of incipient periodontitis among young smokers and non-smokers by measuring the distance between cement-enamel junction and alveolar crest (CEJ-Ac) using Cone Beam Computed Tomography (CBCT). Material and methods: The total sample composed of fifty two participants, thirty one smokers and twenty one non-smokers (age range 14-22 years). Periodontal parameters: plaque index (PLI), gingival index (GI) were recorded for all teeth exc

Porosity is important because it reflects the presence of oil reserves. Hence, the number of underground reserves and a direct influence on the essential petrophysical parameters, such as permeability and saturation, are related to connected pores. Also, the selection of perforation interval and recommended drilling additional infill wells. For the estimation two distinct methods are used to obtain the results: the first method is based on conventional equations that utilize porosity logs. In contrast, the second approach relies on statistical methods based on making matrices dependent on rock and fluid composition and solving the equations (matrices) instantaneously. In which records have entered as equations, and the matrix is sol

In our article, three iterative methods are performed to solve the nonlinear differential equations that represent the straight and radial fins affected by thermal conductivity. The iterative methods are the Daftardar-Jafari method namely (DJM), Temimi-Ansari method namely (TAM) and Banach contraction method namely (BCM) to get the approximate solutions. For comparison purposes, the numerical solutions were further achieved by using the fourth Runge-Kutta (RK4) method, Euler method and previous analytical methods that available in the literature. Moreover, the convergence of the proposed methods was discussed and proved. In addition, the maximum error remainder values are also evaluated which indicates that the propo