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 minimizing the degree of error between approximate and exact solutions. The Wang-Ball series has shown its usefulness in solving any real-life scenario model as first- or second-order differential equations (DEs).
ABSTRACT
Learning vocabulary is a challenging task for female English as a foreign language (EFL) students. Thus, improving students’ knowledge of vocabulary is critical if they are to make progress in learning a new language. The current study aimed at exploring the vocabulary learning strategies used by EFL students at Northern Border University (NBU). It also aimed to identify the mechanisms applied by EFL students at NBU University to learn vocabulary. It also aimed at evaluating the approaches adopted by EFL female students at Northern Border University (NBU) to learn a language. The study adopted the descriptive-analytical method. Two research instruments were developed to collect data namely, a survey qu
... Show MoreThis study investigated the outcome of Alstonia boonei stem bark on liver enzymes after inducing the Wistar albino rats with carbon tetrachloride (CCl4). This effect of plant extract was compared with silymarin – a drug commonly used for the treatment of chronic hepatocyte disorder. The plant sample was extracted with ethanol; acute toxicity study of the extract was performed on eighteen Wistar mice, while 30 rats were sacrificed for liver enzymes assay. The rats were divided into six clusters: each cluster has five rats, culster 1 served as control and was given 2 mL/kg b.w - distilled water; clusters 2 – 6 were CCl4 induced. Cluster 2 was untreated but served as the negative control while cluster 3 wa
... Show MoreThe research aims to achieve a set of objectives, the most important of which is to educate the management of companies operating in the private sector about the advantages and risks of using creative accounting practices, as on the one hand they serve the interests of the company and improve its image, and on the other hand it exposes it to the risks of non-compliance with tax laws and legislation or the risks of default and bankruptcy as a result of exploiting gaps and flexibility in the application Accounting standards, and in line with the objectives and through the research problem that was formulated in the form of a question (Are their creative accounting practices that are reflected in the honesty and fairness of financia
... Show MoreMany undergraduate learners at English departments who study English as a foreign language are unable to speak and use language correctly in their post -graduate careers. This problem can be attributed to certain difficulties, which they faced throughout their education years that hinder their endeavors to learn. Therefore, this study aims to discover the main difficulties faced by EFL students in language learning and test the difficulty variable according to gender and college variables then find suitable solutions for enhancing learning. A questionnaire with 15 items and 5 scales were used to help in discovering the difficulties. The questionnaire was distributed to the selected sample of study wh
... Show MoreIraqi agriculture faces a major water problem, affecting cultivated areas, agricultural production, farmers’ incomes and food security. However, the results achieved in rationalizing the use of irrigation water are still limited and do not match what they should be in order to meet this serious challenge. The study aimed to provide a vision for the development of the effectiveness of the dissemination of innovations to rationalize the use of irrigation water in Iraqi agriculture. In light of the framework of the dissemination of agricultural innovations, factors related to their effectiveness, and the summary of the Iraqi experience in the field of dissemination of modern irrigation
Abstract
The research aimed to prepare an audit program focusing on the activities of municipal institutions related to the environmental dimension as one of the dimensions of sustainable development, and applying the program for the purpose of preparing an oversight report related to assessing the impact of the activities of municipal institutions on the environmental reality as the main channel through which municipal institutions contribute to achieving the part related to it. Among the requirements of sustainable development, the proposed program was prepared and applied to the institutions affiliated to the Directorate of Mu
... Show MoreThe current study investigates the role of smart sports bracelets on physical and motor skills development among youth volleyball players, closing the research gap of wearable technology in sport training. Understanding the necessity of up-to-date training measures of handicaps for perfection of athletic performance, the research is focused on comparison of the effect of strength, agility and flexibility achieved with the use of smart sports bracelet with real time feedback (test group) and without (control group). The research adopted a quasi-experimental design through a sample of (12) players et al.-Karkh Sports Club, (6) of them were in the experimental group (who used the smart bracelet) and (6) of them were in the control group (who u
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