Dissertations/Theses - Department of Mathematics
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Item New approach to partial differential approximants(Department of Mathematics, BUET, 2004-12) Mustafizur Rahman, Md.; Abdul Hakim Khan, Dr. Md.The modellmg of physical phenomena usually results to nonlinear problems whose solutions may have singularities Practically tile locations of tile singularities are important for many problem" a solution can be Iuwld as a series in powers of one or ~everal independent variable" In this thesis under the title "A New Approach To Partial Differential ApprOXllnanto" we ha,e analysed series L11pItem Numerical prediction of hydrodynamics characteristics of modern marine propulsive device in steady flow(Department of Mathematics, BUET, 2009-03) Kamrul Hasan, Mohammad; Abdul Hakim Khan, Dr. Md.A potential based Surface Panel Method (SPM) is applied to the hydrodynamic analysis of modern marine propuslve device, i.e., podded propulsion system (PI'S) in steady flow. At first the surface of the body is approximated by a number of small hyperboloidal quadri lateral panel, with constant sources and doublet distributi(ms. The surface of the trailing vortex sheet is also represented by hyperboloidal quadrilateral panels with constant doublet distributions. The strengths of sourceItem Study of dominating singularity behavior of series using computer based approximation techniques(Department of Mathematics, BUET, 2007-04) Rifat Ara Rouf; Abdul Hakim Khan, Dr. Md.Very few nonlinear probkms can be solved exactly but it is sometimes possible to expand solution in powers of some parameters. In practice the presence of singularities pre~ents rapid convergence of lhe series, so it lS necessary to seck an efficient approximate method. Our purpose is to analyze the dominating singularity behavior of a few problems and the performance of approximate methods. The aim of this thesis is to analyze the approxImate methods by applying them to various model problems, Firstly, we have applied them to some standard problems, whose singularities are known. Secondly we have analyzed numerically the critical behavior of the solutions 0r two non-linear ditTercntiaiequations. Finally, we have studied the fklwina porous pipe with dcce1eratmgwall for analy~ingthe dominant singularity behavior of the flow. The series related to the Reynolds number R is developed by using algebraic programming language MAPLE, The series i, then analyzed by variou, generalizations of the approximate methods. We observe that the convergence or both the series 1S limited by the dominating singularity located at R = R, '" 3,0724980042 and surprisingly there IS another turning point at R, '" 8.813114939 .The result concluded that there is a reversal now at the walL