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).
Годы, принадлежащие концу XIX – началу XX столетия, вошли в русскую литературу под красивым названием Серебряный век. В это время в стране появился целый ряд выдающихся поэтов, имена которых навсегда останутся в русской и мировой литературе. Это Ахматова, Гумилев, Блок, Маяковский и многие другие. Все эти люди творили в нелегкое для России время. Началом Серебряного века условно считают 189
... Show MoreThis research was one of the terms that used by Al-Bazzar in his musnad and this term was (Al-azza) who launched on some ways and hadiths and I collected those narration, and I have graduated and studied it to access to the meaning which Al-Bazzar want that from this description. In the introduction of the research, I have mention the importance of the subject and the reasons for his selection and also my plan, a preface where I mentioned the definition of Al-Bazzar and his musnad, then in the first section I defined Al-azza linguistically and idiomatically , the second section I studied the hadiths that Al-Bazzar described them with azza ,and then I conclude it with my results that I have reach
... Show MorePraise be to God, prayer and peace be upon the Messenger of Allah and after:
The science of interpretation is related to the book of God Almighty; it is considered one of the most honorable sciences. It started with a long time ago. In the early days of Islam, the area of the Islamic state expanded. The people entered the religion of Allah in groups. In the language, and people do not know more than the meanings of the Koran was the need to write in this scie234nce is strong, and perhaps the first of the thousand in the (meanings of the Koran) Abu Ubaida in his book (metaphor of the Koran), Abu Ubaida was affected by his specialization in Arabic science, Prominent on his book.
The second section wa
... Show Moreسعي المجتمع العراقي منذ أكثر من نصف قرن مضى لإعادة استثمار عشرات المليارات من الدولارات من الإيرادات النفطية في القطاع الزراعي وهياكله وبنياته التحية، كإنشاء السدود والخزانات المائية واستصلاح الأراضي والمشاريع الإنتاجية الحيوانية والنباتية وبطاقات كادت تقترب او تتجاوز حاجز طلب السكان من الأغذية والمنتوجات الزراعية التي تغذي الصناعة الا ان الزيادة السكانية وتحسن مستوى الدخل النفطي شكلا انتقالا جدي
... Show Moreتتزايد الصعوبات التي يعاني منها الطالب بشكل خاص والتدريسي بشكل عام في المرحلة الراهنة وذلك لنقص المصادر والكوادر العلمية الرصينة التي كانت تفخر بها جامعات العراق ولا سيما جامعة بغداد اذ أن الجامعات هي اعلى قيمة في السلم التعليمي وتعد بيئة نقية أوجدها المجتمع للتربية من خلال المناهج الدراسية التي تؤدي بشكل سليم وان الجامعة بوصفها سياقاً اجتماعياً لها أهمية في التشجيع على الإبداع وتعد جيلاً من الشباب للعمل
... Show MoreThe numerical response of Chrysoperla mutata MacLachlan was achieved by exposing the larvae of the predators to various densities of dubas nymphs Ommatissus lybicus DeBerg. Survival rate of predators’ larvae and adults emergence increased with increasing consumption . Repriductive response of predator was highly correlated with the amount of food consumed (+0.996).
This work predicts the effect of thermal load distribution in polymer melt inside a mold and a die during injection and extrusion processes respectively on the structure properties of final product. Transient thermal and structure models of solidification process for polycarbonate polymer melt in a steel mold and die are studied in this research. Thermal solution obtained according to solidify the melt from 300 to 30Cand Biot number of 16 and 112 respectively for the mold and from 300 to 30 Cand Biot number of 16 for die. Thermal conductivity, and shear and Young Modulus of polycarbonate are temperature depending. Bonded contact between the polycarbonate and the steel surfaces is suggested to transfer the thermal load. The temperat
... Show MoreIn this paper, a least squares group finite element method for solving coupled Burgers' problem in 2-D is presented. A fully discrete formulation of least squares finite element method is analyzed, the backward-Euler scheme for the time variable is considered, the discretization with respect to space variable is applied as biquadratic quadrangular elements with nine nodes for each element. The continuity, ellipticity, stability condition and error estimate of least squares group finite element method are proved. The theoretical results show that the error estimate of this method is . The numerical results are compared with the exact solution and other available literature when the convection-dominated case to illustrate the effic
... Show MoreNonlinear differential equation stability is a very important feature of applied mathematics, as it has a wide variety of applications in both practical and physical life problems. The major object of the manuscript is to discuss and apply several techniques using modify the Krasovskii's method and the modify variable gradient method which are used to check the stability for some kinds of linear or nonlinear differential equations. Lyapunov function is constructed using the variable gradient method and Krasovskii’s method to estimate the stability of nonlinear systems. If the function of Lyapunov is positive, it implies that the nonlinear system is asymptotically stable. For the nonlinear systems, stability is still difficult even though
... Show MoreIn this research the natural frequency of a cracked simple supported beam (the crack is in many places and in different depths) is investigated analytically, experimentally and numerically by ANSYS program, and the results are compared. The beam is made of iron with dimensions of L*W*H= (0.84*0.02* 0.02m), and density = 7680kg/m3, E=200Gpa. A comparison made between analytical results from ANSYS with experimental results, where the biggest error percentage is about (7.2 %) in crack position (42 cm) and (6 mm) depth. Between Rayleigh method with experimental results the biggest error percentage is about (6.4 %) for the same crack position and depth. From the error percentages it could be concluded that the Rayleigh method gives
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