كلية العلوم الرياضية والاحصاء
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Item D'Alembert Solution For Wave Equation(Al-Neelain University, 2010) Abd Alfatah Mohammed Osman AbasherAbstract In this research , introduction to wave equation , two new proofs and extensions are proposed . at the same time ,two equivalent equation systems for the wave equation and the corresponding initial value problems are advanced and proved by using the characteristics concepts and methods . and some interesting discussions of the initial –boundary value problems (IBVP) and the different cases for at the boundary point . 5 خلاصة البحث: تطرقنا فى ھذا البحث لمقدمة عن الموجة ، والتوصل للمعادلة التفاضلیة التى تصف حركة الموجة والشروط الابتدائیة لھا من ثم حل ھذه المعادلة التفاضلیة باستخدام اسلوب دالمبرت والذى اعتمدنا فیھ على طریقة تحویل ھذه المعادلة الى نظامین من أنظمة المعادلات التفاضلیة تكافئ ھذه المعادلة . وتطرقنا أیضا لحل دالمبرت لمسائل القیم الابتدائیة والحدیة ، سلوك الموجة عند النقاط الحدیة ، من حیث انھا ثابتة فى الطرفین ، او ثابتة فى طرف ومتحركة فى الاخر أو متحركة فى الطرفین ، تصف ھذه الحركة فى كل حالة . mapleوأخیرا برامج بلغةItem The Algebraic Treatment of Symmetric Spaces(Neelain University, 2008) Nemaat Hamed TalebABSTRACT We study manifolds spaces ‘which lead to Lie group, then by definition of transitive action of a Lie group in a manifold we get homogeneous spaces. ' Also we study symmetric spaces, which are particular homogeneous spaces. We classify simple Lie algebra over C according to Dykin diagram. Also by means of real form we classify simple Lie algebra over IR. We show that every symmetric space gives rise to an orthogonal symmetric Lie algebra. Finally we classify Riemannian symmetric spaces of types I, II, III and IV according to the classification of the irreducible orthogonal symmetric Lie algebra of types I, II, III, and IV.Item The Algebraic Treatment of Symmetric Spaces A thesis submitted(Neelain University, 2008) Nemaat Hamed TalebABSTRACT We study manifolds spaces which lead to Lie group, then by definition of transitive action of a Lie group in a manifold we get homogeneous spaces. Also we study symmetric spaces, which are particular homogeneous spaces. We classify simple Lie algebra over C according to Dykin diagram. Also by means of real form we classify simple Lie algebra over DR. We show that every symmetric space gives rise to an orthogonal symmetric Lie algebra. Finally we classify Riemannian symmetric spaces of types I, II, III and IV according to the classification of the irreducible orthogonal symmetric Lie algebra of types I, II, III, and IV.Item Analysis of a Mathematical Model of Malaria Disease(2018-01) Mohamed Kamalaldin Mohamed BabekirAbstract Malaria is one of the deadliest diseases around the world causing the death of around 429,000 person in the year 2015 only. This led the scientists around the world to work hard to fight against the disease. In this study, we analyzed the mathematical model of malaria transmission. We calculated R0 which could determine the future of the disease. We examined two sets of parameters, low prevalence and high prevalence and we calculated the effect rate of all parameters using sensitive analysis. Numerical simulations are carried out to confirm the analytical results and explore the possible behavior of the formulated model.Item And classification of Lie algebras On the characterization(Al-Neelain University, 2016) Anwar Adam Ahmed MohammedAbstract In this work we studied Lie groups and Lie algebras. We Considered several examples of Lie groups and their associated Lie algebras .We treated the representation theory of Lie groups And used this theory in the problem of classification of some Lie algebras such as semi simple and solvable Lie .algebras .Other Lie algebras have also been characterized 5 المستخلص في هذا البحث درسنا زمر لي وجبر لي. تناولنا عدة امثلة لزمر لي وجبر لي المتعلقة بتلك الزمر. عالجنا نظرية التمثيل لزمر لي وإستخدمنا هذه النظرية في مسألة تصنيف بعض جبر لي كجبر شبه بسيط وكذلك جبر قابلية الحل. كما تم تصنيف جبر لي اخرItem APPLICATION OF - " THE VIRIAL METHOD TO THE SOLUTION OF SOME PROBLEMS < ' IN FLUID DYNAMICS(Alneelain University, 2006) Mohamed Saad E1-Din Abdel Gafoor Abdel MagidThe problem of the charged spheroidal bubble is studied using the virial method. The conditions that are necessary for equilibrium are deduced and the oscillation of the bubble is studied . The frequencies belonging to the second order harmonics are found . Further extension of the virial theorem is made by studying the viscous fluid sphere in an incompressible viscous fluid giving the different and necessary virial equations of motion for both the exterior and the interior media and then the equilibrium state is studied.Item application of homotopy perturbation method to predator-prey models(2016) gehan abdalgafar ahmed mohammedItem Application of la place transform on orddinary and fractional ordianry differential equations(Al-Neelain University, 2014) Samah Abd Elazim Ali\ i Abstract In this thesis we focused on the concept of Ordinary Differential Equations which appears to be important in physical systems, electri- cal mechanical, Fractional Ordinary Differential Equations and other fields, in particular the basic theory of Fractional Ordinary Differential Equations involving Riernman-Liouville operators and some examples explain their applications. The Laplace transform method has been successfully applied to solve the Ordinary and Fractional Ordinary Differential Equati0ns.The method is very powerful and eflicient in finding solution.Item APPLICATION OF LIE GRoUPs IN THE SOLUTION OF SoME ORDINARY DIFFERENTIAL EQUATIONS(ALNEELAIN UNIVERSITY, 2003) MOHAMMED ABD AL—BAcI MOHAMMEDABSTRACT Lie's group theory of diflerential equations was initiated by the Norwegian mathematician Marius Sophus Lie (1842-1899). Today, this area of research is actively engaged. In chapter one of this thesis, we give the fundamental concepts of the one-parameter Lie group of transformations, and it also contains the main theorems and definitions. In chapter two, we apply the Lie's theory to the following second order ODE's x:_v3+xy1-1=0, (1) xiv; —y,: —l = 0. (2) _v: —y1 —£=O. (3) y -t:(1”:+,t:_v]: — Zxyl + 2 = 0 . (4) k d y h . = i . k = 1.2. w ere y_ LN In this chapter. we obtain the following results (i) The symmetry groups of(1), (2). (3). and (4). (ii) Reduce the order of (1). (2), (3), and (4) to the first order ordinary differential equations. (111) The general solution of (1). (2), (3), and (4). In chapter three, we considered the non-linear third order ODE y;+Zyy:-_v|2=O. (5)where _vk which is k In this cha (i) (ii) Red equ (m) The (iv) Ne The symmetry groups of (0) w __-Q _ ,___ _ k — d f k -1 v 3 dx nown as Goldstein equation [7]. pter, we obtain the following results uce the order of (5) to the first order ordinary diflerential ation. invariant solutions of (5). solutions from known solutions for (5). IVItem Application of Spectral Adomian Decomposition Method on Heat and Mass Transfer of Boundary Layer(Al-Neelain University, 2015) Salma Hassan Mohammed HassanAbstract In this study, we proposed numerical method for solving non-linear differential equations. The method is hybired of spectral and Adomian decomposition method. The method will applied on the problem of convection heat and mass transfer, the convergence of the method tested and displayed on tables. The velocity, temperature and concentration have been obtained and discussed for various physical parameter.Item APPLICATION OF SPECTRAL HOMOTOPY PERTURBATION METHOD ON BOUNDARY LAYER FLOW WITH RADIATION EFFECT(Al-Neelain University, 2015) Abdalaziz Elhaj Bakhit ElkhwadAbstract In this thesis we study the effect of radiation on the boundary layer flow and heat transfer of viscous fluid. The Spectral Homtopy Perturbation Method (S-HPM) used to solve the system of the governing equations. We also determine the convergent series of the solution. The accuracy and rate of convergence of the solution has been tested and compared for different orders and the results are presented in tables . The physical interpretation to these expressions is assigned through graphs.Item Application of Spectral Quasilinearization Method on Fluid Flow(Al-Neelain University, 2015) Hisham Ali Ahmed GhanimAbstract In this thesis, we solve the problem of Soret and Dufour effects on mixed convection from an exponentially stretching surface of the flow of viscous incompressible fluid. The method of Quasilinearization is used to solve the problem described the flow. The method is very simple and effective and can be used instead of traditional numerical methods.Item Application of the Spectral Local Linearization Method on a System of Nonlinear Ordinary Di erential Equations(Alneelain University, 2016-12) Abubakr Eltayeb Mohammed EltayebIn this study the problem of unsteady nano uid ow over a stretching sheet subject to couple stress e ects is presented. Instead of assuming that the nano-particle volume fraction at the boundary surface may be actively controlled, a realistic boundary condition for the nanoparticle volume fraction model is that the nano-particle ux at the boundary be set to zero. We assume there is no active control of the nano-particle volume fraction at boundary. The spectral local linearisation method has been used to solve the governing equations, moreover the results were further con rmed by using the quasi-linearization method. The qualitative and quantitative e ects of the dimensionless parameters in the problem such as the couple stress parameter, the Prandtl number, the Brownian motion parameter, the thermophoresis parameter and the Lewis number on the uid behavior are determined. iItem Application of the Spectral Local Linearization Method on a System of Nonlinear Ordinary Differential Equations(Al-Neelain University, 2016) Abubakr Eltayeb Mohammed EltayebAbstract In this study the problem of unsteady nanofluid flow over a stretching sheet subject to couple stress effects is presented. Instead of assuming that the nano-particle volume fraction at the boundary surface may be actively controlled, a realistic boundary condition for the nanoparticle volume fraction model is that the nano-particle flux at the boundary be set to zero. We assume there is no active control of the nano-particle volume fraction at boundary. The spectral local linearisation method has been used to solve the governing equations, moreover the results were further confirmed by using the quasi-linearization method. The qualitative and quantitative effects of the dimensionless parameters in the problem such as the couple stress parameter, the Prandtl number, the Brownian motion parameter, the thermophoresis parameter and the Lewis number on the fluid behavior are determined. ivItem Application of the successive linearization method to micropolar flow in a porous channel(2016) Mohammed Ahmed Ali Mohammed Ahmed MohammedAbstract In this study the successive linearization method is applied to the problem of mi- cropolar flow in a porous channel. The governing partial differential equations are transformed into a system of ordinary differential equations and then solved via SLM. The effects of various parameters are discussed and analysed.Item Application of the successive linearization method to unsteady MHD ow over stretching sheet(Al-Neelain University, 2016) Mona Jaafar Elamin AhmedAbstract The aim of this study is to present the unsteady magnetohydrodynamic (MHD) boundary layer flow and heat transfer of a fluid over a stretching sheet in the presence of viscous dissipation and heat source. The governing nonlinear partial differential equations are first transformed into a system of non-linear ordinary differential equations and then solved numerically by the successive linearization method (SLM). Effects of various physical parameters on the velocity and temperature profiles are presented graphically and in tabular form. Numerical comparison is also presented with the existing results in literature which shows that the present results are in an excellent agreement.Item APPLICATIONS OF BANACH FIXED POINT THEOREM AND APPROXIMATION THEORY(Al-Neelain University, 2004) Moram Adam MohammedAbstract This dissertation consists of four chapters : In chapter one we present concept of fixed point and some examples of it and discusses the Banach fixed point theorem and some definitions in a metric space . The second chapter is devoted to applications of Banach fixed point theorem . In chapter three we present approximation in normed spaces and deals with problem of existence and uniqueness of best approximation . In last chapter we define the uniform approximation and present a brief introduction about approximation in Hilbert spaces and Chebyshev polynomials.الخلـصــــــــة هذه الرسالة تتكون من اربعة فصول : الفصل اللول: يقدم تعريـف للنقطـة الثابتــة لوبعـض المثلة عليها لويناقش مبرهنة باناخ للنقطة الثابتة لوبعـض التعريفات في الفضاء المتري . الفصل الثاني : مخصص لتطبيقات نظريــة النقطــة الثابتة لباناخ . الفصــل الثــالث : يقــدم نظريــة التقريــب علــي الفضاءات المنتظمة لويعالج مشكلة الوجــود لوالوحدانيــة للتقريب الحسن . الفصل الرابـع : يعــرف التقريــب المنتظــم لويقــدم مقدمــة مــوجزة عــن التقريــب فــي فضــاءات هلــبرت لوكثيرات حدلود تشيبشف .Item Applications of Caputo derivatives and Homotopy Perturbation Method in Fractional Calculus(Al Neelain University, 2018-03) Nabil Sulaiman Ebrahim AbdulazizThe aim of this study is to study fractional derivatives by Caputo and Mainardi. We found the exact solution for the linear and nonlinear Reaction-Diffusion equation by using a Homotopy perturbation method, modified Homotopy perturbation method, Laplace transform and Fourier transform.Item Applications of Conformal map to Potential Theory and Fluid Mechanics(2017-11) Abdalbagy Hatim AlshikhAbstract In this work we study the theory of complex variables . Being motivated by the vast applications of this theory , we considered the analytical properties provided by the theory of complex functions in the field of electrostatics , Fluid mechanics and Harmonic analysis .We introduced the important theorems relating derivatives and integrals such as Cauchy integral formulas . We have also utilized conformal transformations in several applications such as solving Poisson equationItem Applications of Finite Element Method on Beams(Al-Neelain University, 2015) Eman Jamal-Aldeen Alkhair Altahirمستلخص طریقة العناصر المنتھیة ھي عرض بطریقة متغایره لحل المعادلھ التفاضلیھ . نضع فیھا المسألھ المستمره في cjj ،الدالھ التقریبیھ شكل معادلھ تفاضلیھ مكافئة لصیغھ التغایر، ویفترض الحل في صورة تركیب خطي، ھي j . البارمتیرات cj تحدد باستخدام صیغة التغایر . طریقة العناصر المنتھیھ تحسن تقنیھ النظام للدالھ التقریبیھ لمجال بسیط مركب ھندسیا . في طریقة العناصر المنتھیة، الدالھ التقریبیھ ھي كثیرة حدود (كثیره الحدود تعرف لكل مجال وتسمي بالعنصر) Abstract The finite element method is introduced as a variationaly based technique of solving differential equations. A continuous problem described by a differential equations is put into an equivalent variational from, and the approximate solution is assumed to be a linear combination , Pcjφj , of approximation function φj . The parameters cj a determined using the associated varitional form. The finite element method provides a systematic technique for deriving the approximation function for simple subregions by which a geometrically complex region can be represented. In the finite element method, the approximation function are piecewise polynomials (i.e, polynomials that are defined only on a subregion, called an element)