Fragmentation equations occur naturally in many real world problems, see [ZM85, ZM86, HEL91, CEH91, HGEL96, SLLM00, Ban02, BL03, Ban04, BA06] and references therein. Mathematical study of these equations is mostly concentrated on building existence and uniqueness theories and on qualitative analysis of solutions (shattering), some effort has be done in finding solutions analytically. In this project, we deal with numerical analysis of fragmentation equation with transport. First, we provide some existence results in Banach and Hilbert settings, then we turn to numerical analysis. For this approximation and interpolation theory for generalized Laguerre functions is derived. Using these results we formulate Laguerre pseudospectral method and provide its stability and convergence analysis. The project is concluded with several numerical experiments. / Thesis (M.Sc.)-University of KwaZulu-Natal, Durban, 2012.

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Wind energy forecasting can facilitate wind energy integration into a power system. In particular, the management of power system security would benefit from forecast information on plausible large, rapid change in wind power generation. Numerical Weather Prediction (NWP) systems are presently the best available tools for wind energy forecasting for projection times between 3 and 48 hours. In this thesis, the types of weather phenomena that cause large, rapid changes in wind power in southeast Australia are classified using observations from three wind farms. The results show that the majority of events are due to horizontal propagation of spatial weather features. A study of NWP systems reveals that they are generally good at forecasting the broad large-scale weather phenomena but may misplace their location relative to the physical world. Errors may result from developing single time-series forecasts from a single NWP grid point, or from a single interpolation of proximate grid points. This thesis presents a new approach that displays NWP wind forecast information from a field of multiple grid points around the wind farm location. Displaying the NWP wind speeds at the multiple grid points directly would potentially be misleading as they each reflect the estimated local surface roughness and terrain at a particular grid point. Thus, a methodology was developed to convert the NWP wind speeds at the multiple grid points to values that reflect surface conditions at the wind farm site. The conversion method is evaluated with encouraging results by visual inspection and by comparing with an NWP ensemble. The multiple grid point information can also be used to improve downscaling results by filtering out data where there is a large chance of a discrepancy between an NWP time-series forecast and observations. The converted wind speeds at multiple grid points can be downscaled to site-equivalent wind speeds and transformed to wind farm power assuming unconstrained wind farm operation at one or more wind farm sites. This provides a visual decision support tool that can help a forecast user assess the possibility of large, rapid changes in wind power from one or more wind farms.

Thesis (Ph. D.)--University of Texas at Austin, 2008. / Vita. Includes bibliographical references.

Thesis (M.Phil.)--Hong Kong University of Science and Technology, 2008. / Includes bibliographical references (leaves 59-61). Also available in electronic version.

Thesis (Ph. D.)--University of Hong Kong, 2005. / Also available in print.

Thesis (Ph. D.)--University of Washington, 1996. / Vita. Includes bibliographical references (p. [126]-132).

Thesis (M.S.)--Worcester Polytechnic Institute. / Keywords: caustics; turbulence; wave propagation; ultrasonic flow meter. Includes bibliographical references (p. 82-84).

Thesis (M.S.)--Worcester Polytechnic Institute. / Keywords: PDE-constrained optimization; O3D; sundance; source inversion. Includes bibliographical references (p. 77-78).