Masters theses : Statistics
Permanent URI for this collectionhttps://repository.neelain.edu.sd/handle/123456789/12105
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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 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 ODE