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On Qualitative Properties And Convergence Of Time-Discretization Methods For Semigroups, Mihaly Kovacs

LSU Doctoral Dissertations

In this dissertation we use functional calculus methods to investigate convergence and qualitative properties of time-discretization methods for strongly continuous semigroups. Stability, convergence, and preservation of contractivity (or norm-bound) of the semigroup under time-discretization is investigated in a Banach space setting. Preservation of positivity, concavity and other qualitative shape properties which can be described via positivity are treated in a Banach lattice framework. The use of the Hille-Phillips (H-P) functional calculus instead of the Dunford-Taylor functional calculus allows us to extend fundamental qualitative results concerning time-discretization methods and simplify their proofs, including results on multi-step schemes and variable step-sizes. We …