This paper presents seven modified Adomian Decomposition Method (ADM) techniques for efficiently solving initial value problems, especially those involving non-homogeneous and nonlinear differential equations. While the classical ADM is effective for linear homogeneous cases, it has difficulties solving more complex problems. The proposed modifications—from MADM1 to MLADM—include Maclaurin and Taylor expansions, Laplace transforms, and single-step iterations.• These modifications enhance convergence, reduce complexity, and improve accuracy.• Each method offers specific advantages, such as accelerating convergence (MADM2, RADM4), simplifying computation (TSADM5), and achieving higher accuracy (MLADM).• Numerical examples confirm the accuracy and efficiency of all methods, highlighting their superiority over the classical ADM.
يعد هذا النص أحد النصوص المسمارية المصادرة التي بحوزة المتحف العراقي، ويحمل الرقم المتحفي (235869)، قياساته )12،7x 6x 2،5سم). يتضمن مدخولات كميات من الشعير،أرخ النص الى عصر أور الثالثة (2012-2004 ق.م) و يعود الى السنة الثالثة من حكم الملك أبي-سين (2028-2004 ق.م)،أن الشخصية الرئيسة في هذا النص هو)با-اَ-كا مسمن الماشية( من مدينة أري-ساكرك، ومقارنته مع النصوص المسمارية المنشورة التي تعود الى أرشيفه يبلغ عددها (196) نصاً تضمنت نشاطاته م
... Show MoreKE Sharquie, SA Al-Mashhadani, AA Noaimi, AA Hasan, Journal of Cutaneous and Aesthetic Surgery, 2012 - Cited by 19
This paper proposes a new method to tune a fractional order PID controller. This method utilizes both the analytic and numeric approach to determine the controller parameters. The control design specifications that must be achieved by the control system are gain crossover frequency, phase margin, and peak magnitude at the resonant frequency, where the latter is a new design specification suggested by this paper. These specifications results in three equations in five unknown variables. Assuming that certain relations exist between two variables and discretizing one of them, a performance index can be evaluated and the optimal controller parameters that minimize this performance index are selected. As a case study, a thir
... Show MoreThis paper proposes a new method to tune a fractional order PID controller. This method utilizes both the analytic and numeric approach to determine the controller parameters. The control design specifications that must be achieved by the control system are gain crossover frequency, phase margin, and peak magnitude at the resonant frequency, where the latter is a new design specification suggested by this paper. These specifications results in three equations in five unknown variables. Assuming that certain relations exist between two variables and discretizing one of them, a performance index can be evaluated and the optimal controller parameters that minimize this performance index are selected. As a case study, a third order linear time
... Show MoreThe arrival of Russian President Vladimir Putin to power in the Russian Federation is an important factor in delineating a new approach to Russian policy towards regions that have great strategic importance affecting its national security. Therefore, NATO's progress eastward towards these regions prompts Russia to delineate a new strategy to confront this progress as well as preserving its control in the near neighboring regions represented by the countries of Eastern Europe, especially after the changes that occurred in those regions following the color revolutions that swept the region, such as the first application of this Russian policy in 2014, through the annexation of Crimea, and the latest military operations in Ukraine i
... Show MoreThe present work was done in an attempt to build systematic procedures for treating warts by 810 nm diode laser regarding dose parameters, application parameters and laser safety. The study was done in Al- Kindy Teaching Hospital in Baghdad, Iraq during the period from 1st October 2003 till 1st April 2004. Fifteen patients completed the treatment and they were followed for the period of 3 months. Recalcitrant and extensive warts were selected for the study. Patients were randomly divided into 3 groups to be treated by different laser powers 9, 12 and 15 W, power density of 286 W/cm2, 381W/cm2, 477 W/cm2 pulse duration of 0.2 s, interval of 0.2 s and repeated pulses were used. The mode of application was either circular or radial. Pain oc
... Show MoreTraditional accounting takes only one dimension (economic) in calculating the value added of the company, and all other aspects (including environmental and social) are neglected, and despite the emergence of Sustainability Accounting and the interest of companies in preparing sustainability reports, these reports are suffering from many problems, including multiple metrics used in measuring companies (cash, quantity and lavish). In addition, these reports may reach dozens of pages in some companies and this causes the problem (information overload) which affects the qualitative properties of accounting information such as appropriate and relative, which requires the need to find a tool that can measure the Sustainability Unit of
... Show More