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حول الحلول العددية لمعادلة فريدهولم التكاملية من النوع الثاني == On The Numerical Solution of Fredholm Integral Equation Of Second Kind

Author name: مهند موسى عيسى التميمي
Supervisor name: رياض شاكر نعوم | هادي جابر مصطفى
General topic: Mathematics
Specific topic: Numerical Analysis
Degree: Master
University: Mustansiriyah University - College Of Education For Girls - Department Of Mathematics
Language: English
University location: Baghdad
First pages:
Abstract: تختص هذه الرسالة بدراسة الحلول العددية لمعادلة فريدهولم التكاملية من النوع الثاني . حيث درسنا استقرارية وتقارب طريقتي تحليل النواة وطريقة نيستروم مع انواع مختلفة من الطرق التربيعية (quadrature rules) مثل (شبه المنحرف وسيمبسون التجميعية) وانواع مختلفة من العقد (node points) مثل (النقاط المنتظمة (xi=a+ih) وجذور لحدوديات متعامدة مثل (حدودية شيبيشيف وحدودية ليجندر) ) . ثم درسنا تقارب واستقرارية طريقة كالركن وطريقة كالركن التكرارية مع انواع مختلفة من القواعد(basis) مثل (الحدودية الاعتيادية وحدودية شيبيشيف) وانواع مختلفة من الطرق التربيعية وانواع مختلفة من العقد مثل (النقاط المنتظمة وجذور حدودية شيبيشيف) . ان استقرارية النظام الخطي الذي تم الحصول عليه من تطبيق الطرق اعلاه تم دراستها باستخدام تعريف العدد الشرطي وكذلك حساب الحد الاعلى للخطا النسبي لعدة مسائل من ضمنها المعتلة الضعيفة (weak singular problem) . قمنا بالمقارنة بين الطرق اعلاه لعرض اي الطرق اكثر ملائمة لايجاد الحل التقريبي لمعادلة فريدهولم التكاملية من النوع الثاني | This thesis is concerned with the numerical solution of a linear Fredholm integral equation of second kind. We study the stability and convergence of the Degenerate kernal method and Nystrom method with : - Different type of quadrature rule (e.g., Combined Trapezoidal and combined Simpson). - Different type of node points such as uniform points and zero’s of orthogonal polynomial (e.g., Chebyshev and Legendre).Also we study the convergence and stability of the Galerkin method and Iterate Galerkin method for Fredholm integral equation of second kind (with weak singularity or without) with : - Different type of basis function (polynomial or orthogonal polynomial). - Different type of quadrature rule. - Different type of node points such as (uniform node points (xi  a + ih) and zero’s of Chebyshev polynomial).The stability of the linear system, which arises from applying the above methods has been studied by using the definition of the condition number, , where the upper bound for the relative error has been computed for many problems.To show which method is more suitable to be applied for a (FIE2), a comparison has been made between these methods

التوسيعات الراشدة والاغمارية == RATIONAL EXTENSIONS AND INJECTIVITY

Author name: مهدي صالح نايف
Supervisor name: مهدي صادق عباس
General topic: Mathematics
Specific topic: Mathematics
Degree: Doctorate
University: Mustansiriyah University - College Of Education For Girls - Department Of Mathematics
Language: English
University location: Baghdad
First pages:
Abstract: In this work, many of generalizations of injectivity are introduced and studied by using rational submodules and rationally closed submodules. The nation of (pseudo - ) injective modules is generalized to that of rationally (pseudo - )injective modules. On the other hand, the notions of (quasi - )injective modules and pseudo - injective modules are also generalized to that of RC - (quasi - )injective and pseudo - RC - injective modules respectively.Numerous properties and characterizations of these generalizations are given. Moreover, the relation between these notions is studied. Several known modules are characterization in terms of some of these concepts such as semisimple, rationally extending. Also, sufficient conditions for a direct sum of two rationally extending modules to be rationally extending are considered. The connections between some of these concepts and some other modules such as Hopfain, Co - Hopfain, divisible modules are discussed. Also, semisimple artinian rings, SI - rings have been characterized in terms of some of these concepts.