كلية العلوم الرياضية والاحصاء
Permanent URI for this communityhttps://repository.neelain.edu.sd/handle/123456789/623
Browse
7 results
Search Results
Item Spectral Local Linearisation Method For Hydromagneto-Maxwellian Fluid Flow(Alneelain University, 2022-01) Layla Ibrahim Musa IbrahimAbstract In this work we studied the boundary layer flow of Maxwell fluid on the surface of a solid plate under the effect of a magnetic filed. To simplify the model, the boundary layer approximations have been used and then introduced a similarity transformation to transform the non-linear par- tial differential equations into highly ordinary differential equations. By applying the spectral local linearisation method on the resultant system of differential equation subject to appropriate boundary conditions we obtained accurate numerical solutions with a few iterations. The con- vergence of the SLLM has been tested by calculating the local error between each two iterations. Effects of the governing parameters such as the magnet field M and Deborah number β on the velocity components as well as the skin friction were analyzed in tabular and graph style. We observed that with the increase of magnet field M , the Lorentz drag force in which formed and generated mainly due to a major increase in the thickness of boundary layer, and hence the liquid becomes more viscous which leads to decease in the velocity between its particles due to their closeness to each other. On the other hand we found that for high Deborah number β the material behavior ensures more flexibility.Item symmetry condition of algebraic differential equations(Neelain University, 2005) mnahil mohammed bashierThis study deals with the application of symmetry concept of the solution of the differential equations. The study covers the meaning of symmetry for the differential equation and it gives some examples of it, for centain group especially the rotation group in theplane. »=~ - ~ ~-’ " " We examine if a centain group represents symmetry group of a differential equation, by considering the differential equation as algebraic equation. This is done by studding the partial derivatives of the dependent variables with respect to the independent variables. This leads to consider space called Jet space. The differential equation is a kernel of a map, whose kernel is in fact subspace of the Jet space, which is invariant under group prolongation G, the symmetry group for differential equation. The study introduced some basic concepts which we need to calculate the symmetry group for the differential equations. One of these is the infinitesimal generator for the one parameter group. For this we consider the vector fields with some examples and we give the important features of it. We also provide the criterion of the group G to be a symmetry group for the differential equation. We calculate the symmetry group for the heat equation and we define all the one parameter groups which represent the symmetry of heat equation and we conclude-with the general form of the solution of the heat equation. i To prove this utility we studied the integration theory of ordinaiy differential equation through the symmetry concept. The theory shows that this concept unified several ways for solving the differential equation of first order especially the ideas of separation of variables and exactness which represent the basis of solving the first ODE.Item Optimality Problem of Portfolio in an Incomplete Markets(Al Neelain University, 2015-07) Budoor Mohammed Abd ElatiThe main objective of this thesis is to study the optimal portfolio problem in incomplete markets. The problem of finding such optimal ponfolio is of connection to solve partial differential equations corresponding to the infinitesimal generator of the process describing the risky assets in the given markets.Is the method used to find the solution of the a rising partial differential equation is a viscosity concept .As an application for finding optimal portfolio a consumption problem is considered. Due to the incompleteness of the markets they the problem is challenging because the best strategy We aim will not be perfect.Item symmetry condition of algebraic and differential equations(Neelain University, 2005) mnahil mohammed bashierThis study deals with the application of symmetry concept of the solution of the differential equations. The study covers the meaning of symmetry for the differential equation and it gives some examples of it, for centain group especially the rotation group in theplane. »=~ - ~ ~-’ " " We examine if a centain group represents symmetry group of a differential equation, by considering the differential equation as algebraic equation. This is done by studding the partial derivatives of the dependent variables with respect to the independent variables. This leads to consider space called Jet space. The differential equation is a kernel of a map, whose kernel is in fact subspace of the Jet space, which is invariant under group prolongation G, the symmetry group for differential equation. The study introduced some basic concepts which we need to calculate the symmetry group for the differential equations. One of these is the infinitesimal generator for the one parameter group. For this we consider the vector fields with some examples and we give the important features of it. We also provide the criterion of the group G to be a symmetry group for the differential equation. We calculate the symmetry group for the heat equation and we define all the one parameter groups which represent the symmetry of heat equation and we conclude-with the general form of the solution of the heat equation. i To prove this utility we studied the integration theory of ordinaiy differential equation through the symmetry concept. The theory shows that this concept unified several ways for solving the differential equation of first order especially the ideas of separation of variables and exactness which represent the basis of solving the first ODEItem The Theory of Lie Algebra with Some Applications(Al-Neelain University, 2016) Amir Bashir Mohammed AliAbstract: Lie algebras and their representations are very important to study several problems in mathematics, physics and Sciences. Lie algebra is an associated algebra of a Lie group, that is usually a symmetry group of a problem, such as a differential equation. In this study we gave alternative descriptions of Lie algebra. The descriptions are analytical, algebraic and geometrical. For instance a Lie algebra is a tangent space to the identity to a Lie group. For the sake of applications of Lie algebra we concentrated on the theory of representations of Lie algebras. IV مستخلص الدراسة إن جبر لي وتمثيالته هام جدا لدراسة المسائل المختلفة في الرياضيات و الفيزياء والعلوم. لقد تم ربط جبر لي بمجموعة لي، حيث طبق هذا الجبر في مسائل عديدة كالمعادالت التفاضلية. في هذه الدراسة قدمنا وصفا تحليليا وجبريا وهندسيا لجبر لي، فمثال الوصف الهندسي لجبر لي يمثل فضاء المماس عند العنصر المحايد. من أجل التطبيق ركزنا على نظرية التمثيل لجبر لي.Item An Introduction To The Finite Element Method (Heat Transfer)(Al-Neelain University, 2014) Amna Bakri Humieda BabekerAbstract In this thesis, we studied finite element method to solve the ordinary and partial differential equations with the boundary values problem (1D,2D). As application of finite element method we use it to solve the equation of heat transfer. الخلةصة في هذا البحث درسنا طريقة العنصر المنتهي لحل مسائل القيم الحديه للمعادل ت التفاضليه العاديه و الجزئيه (بعد واحد -بعدين) .و كتطبيق لهذه الطريقه قمنا بحل معادلة التنتقال الحراري .Item On the solution of the successive linearization method to mixed convection boundary layer flow(Alneelain University, 2017-02) Mousrat Mohammed Elkheir BarakatMixed convection heat and mass transfer along a vertical plate embedded in a power- law fluid saturated Darcy porous medium with chemical reaction and radiation effects is studied. The governing partial differential equations are transformed into ordinary differential equations using similarity transformations and then solved numerically using successive linearization method. A parametric study of the physical parameters involved in the problem is conducted and a representative set of numerical results is illustrated through graphs and tables.