<p>Daftardar Gejji and Hossein Jafari have proposed a new iterative method for solving many of the linear and nonlinear equations namely (DJM). This method proved already the effectiveness in solved many of the ordinary differential equations, partial differential equations and integral equations. The main aim from this paper is to propose the Daftardar-Jafari method (DJM) to solve the Duffing equations and to find the exact solution and numerical solutions. The proposed (DJM) is very effective and reliable, and the solution is obtained in the series form with easily computed components. The software used for the calculations in this study was MATHEMATICA^® 9.0.</p>

The method of operational matrices based on different types of polynomials such as Bernstein, shifted Legendre and Bernoulli polynomials will be presented and implemented to solve the nonlinear Blasius equations approximately. The nonlinear differential equation will be converted into a system of nonlinear algebraic equations that can be solved using Mathematica®12. The efficiency of these methods has been studied by calculating the maximum error remainder ( ), and it was found that their efficiency increases as the polynomial degree (n) increases, since the errors decrease. Moreover, the approximate solutions obtained by the proposed methods are compared with the solution of the 4th order Runge-Kutta method (RK4), which gives very

Research indicates that the second half of the twentieth century marked large interests in the service industry by government and private organizations in that one, and the service industry has become the bedrock of plans in achieving economic and social development. From this standpoint felt specialists and researchers the importance of transport modes, including rail, which should be available between Almnltq Civil populated as services organized by the competent authorities to achieve the active participation of citizens in economic and social development in the region and that the term services means economic activities, which are the results Pollack concrete such as accepting the situation and satisfaction them or satisfacti

Abstract

    All of us are indispensable for this rule (the most important and important) individuals, whether we were groups of leaders or followers of peoples or countries because the rule provides adequate guarantees for the correct positions and drawing the plan for successful decision-makers matching with the balances of Sharia without incompatibility between religious or worldly interests or legal positions and therefore in the framework of the most important appointment And distinguish it from the important from the interests or the appointment of the most important and distinguish from the important from the evils and through this rule we learn about the scientific and practical solutions t

في هذا البحث، تم تنفيذ الطريقة الحسابية الفعالة (ECM) المستندة إلى متعددة الحدود القياسية الأحادية لحل مشكلة تدفق جيفري-هامل غير الخطية. علاوة على ذلك، تم تطوير واقتراح الطرق الحسابية الفعالة الجديدة في هذه الدراسة من خلال وظائف أساسية مناسبة وهي متعددات الحدود تشيبشيف، بيرنشتاين، ليجندر، هيرمت. يؤدي استخدام الدوال الأساسية إلى تحويل المسألة غير الخطية إلى نظام جبري غير خطي من المعادلات، والذي يتم حله بع

Summary
This research is included in the study of one of the most important rules of jurisprudence, which is (necessity descends the status of necessity, controls and applications) branching from the major rule (hardship brings facilitation) and since the jurisprudential rule is defined as knowledge of a total or majority rule that applies to all its parts. He has to know all the branches that fall under him, which leads to understanding Sharia, controlling jurisprudential issues and linking them to its rules, so that no contradiction occurs, and he has the jurisprudential faculty that he promotes in consideration and diligence. And what is meant by need: is what is lacking in terms of expansion and raising the distress that often lea

The techniques of fractional calculus are applied successfully in many branches of science and engineering, one of the techniques is the Elzaki Adomian decomposition method (EADM), which researchers did not study with the fractional derivative of Caputo Fabrizio. This work aims to study the Elzaki Adomian decomposition method (EADM) to solve fractional differential equations with the Caputo-Fabrizio derivative. We presented the algorithm of this method with the CF operator and discussed its convergence by using the method of the Cauchy series then, the method has applied to solve Burger, heat-like, and, couped Burger equations with the Caputo -Fabrizio operator. To conclude the method was convergent and effective for solving this type of

the bank sect for any country  is very important  because  its represent a major  nerve   to feed a verity economic and finance activities .development any state measure by development  banking  sets and its represent  important  factor to investors attract . and because  important  of this subject ,teen accounting rule is a specialized for it .its related by  Disclosures in the Financial Statements Of Banks and The Similar Institutions, its accredit  by auditing and accounting standard  consul in republic of Iraq.in date 10/28/1998.                      &

The research discusses the issue of attribution to the verb, because the Arab scholars are unanimous in preventing attribution of the verb, because it is always informed of it, and does not inform about it, but this consensus violates the linguistic use. The research discusses this matter.