Master of Science in Applied Mathematics
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- ItemModeling heat transfer in a metallic plate:(Kampala International University, School of Engineering and Applied Science, 2016-08) Hussaini, Abubakar MuhammadThis work has formulated and developed models for predicting the temperature distributions and the distortions induced in metallic plates by the heat transfer process. Fouriers series of heat conduction equation was considered by using finite difference method.Finite difference models have been developed. Furthermore, a series of load temperature curves for a bead-on-metallic plate have been calculated with suitable convection boundary conditions and material properties. The result form a sparse block tridiagonal matrix,The matrix was program into mathematical computational matrix laboratory MATLAB and came up with numerical results and compared with results obtained from previous research. The effect of different parameters on the heat transfer response, including the temperature speeds, heat inputs,thicknesses of metallic plates.And lastly analysis of error was done and order of con vergence of the error found to be of first order.
- ItemOn the accuracy of the backward difference formula of order four and runge-kutta of order four in solving a first order non-linear ordinary differential equation(Kampala International University, School of Engineering and Applied Sciences, 2016-07) Nweke, Ijeoma AnieIn this study, the researcher investigated if the Runge-Kutta of order 4 method (RK4) is as accurate as the Backward Difference Formula of order 4 (BDF4) in solving a 1st order non-linear Ordinary Differential Equation? Two 1st order non-linear ODE were tested to analyse this problem. The RK4 proved to be more accurate than the BDF4 because the RK4 can generate it’s values without depending on the Analytic method and it showed very slight deviation from the Analytic method when it was rounded off to 9 decimal places, otherwise it was equal to the Analytic method when rounded off to 7 decimal places in equation 1 and 6 decimal places in equation 2. It shows very slight deviation from the Analytic method while the BDF4, despite it’s using starting values from the Analytic method showed large deviation from the Analytic method even when applied to the two tested problems. Even then, BDF4 is more prefered than the RK4 in solving stiff problems because it is A-Stable and converges easily.
- ItemStationary analysis of the m/m/1 queuing system with two customer subgroups(Kampala International University , School of Engineering and Applied Sciences, 2017) Khatete, MichaelA single server Markovian queuing system called theM=M=1 queuing system with two distinct customer types namely; the constraint customer type and the un-constraint customer type is studied. This model is that of a production system with heteroge- neous customer structures devoid of a single customer in the intersection category group wise. Initially, relevant literature covering methodologies, analysis and results derived for single server production systems are reviewed and a gap identi ed. The gap is that: The application of group theory in the analysis of queuing sys-tems is scarce in the literature. This is against the backdrop that most customers of service systems of transportation, telecommunications, com-puter systems and other production centers exhibit certain group charac-teristics. This gap motivated us to impose a group structure on customers of the queuing system in question with the property that for the two subgroups considered in this work, their intersection is null. Using the generating function approach, we provided results on the stationary impact of one subgroup on the other. These results are fundamental basis for optimizing performance of sectors and sub-sectors of production centers relative to their distributions and expectations generally.