Analysis and numerical solutions of fragmentation equation with transport.
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Date
2012
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Abstract
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.
Description
Thesis (M.Sc.)-University of KwaZulu-Natal, Durban, 2012.
Keywords
Equations--Numerical solutions., Numerical analysis., Theses--Applied mathematics.