Title: Numerical solution of singular BVPs in ODEs and parapolic PDEs using collocation.
Other Titles: Numerische Lösung von singulären Randwertproblemen gewöhnlicher Differentialgleichungen und parabolischer partieller Differentialgleichung unter Verwendung von Kollokationsverfahren.
Language: English
Authors: Pulverer, Gernot 
Qualification level: Doctoral
Advisor: Weinmüller, Ewa 
Issue Date: 2020
Pulverer, G. (2020). Numerical solution of singular BVPs in ODEs and parapolic PDEs using collocation. [Dissertation, Technische Universität Wien]. reposiTUm. https://doi.org/10.34726/hss.2021.30254
Number of Pages: 250
Qualification level: Doctoral
The main part of this work covers the solution of initial-/boundary value problems of parabolic differential equations. A code for the solution of boundary value problems of ordinary differential equations using collocation is utilized to achieve that. Discretization in time yields a boundary value problem in space for each time step. The boundary value problem gets solved, trying to control step widths in time to satisfy both time and space tolerances. This way the parabolic differential equation can be solved numerically. The Matlab solver is then used for some test problems. To increase the efficiency of the solver a grid adaptation algorithm is developed to improve the performance of the solution of the boundary value problems. Furthermore boundary value problems of different applications will be solved and documented.
Keywords: numerics; ODE; PDE; collocation; singular; BVP; numerical analysis
URI: https://doi.org/10.34726/hss.2021.30254
DOI: 10.34726/hss.2021.30254
Library ID: AC16199675
Organisation: E101 - Institut für Analysis und Scientific Computing 
Publication Type: Thesis
Appears in Collections:Thesis

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