Identifier

etd-07142005-114344

Degree

Doctor of Philosophy (PhD)

Department

Mathematics

Document Type

Dissertation

Abstract

In this work we analyze error estimates for rational approximation methods, and their stabilizations, for strongly continuous semigroups. Chapter 1 consists of a brief survey of time discretization methods for semigroups. In Chapter 2, we demonstrate a new method for obtaining convergent approximations in the absence of stability for strongly continuous semigroups with arbitrary initial data. In Section 2.2, we state the stabilization result in more general form and show that this method can be used to improve known error estimates by a magnitude of up to one half for smooth initial data. In Section 2.3, we give concrete examples of some of these stabilizers. Section 2.4 concerns abstract stabilization results, including stabilized Trotter-Kato and Lax-Chernoff theorems. In Chapter 3, we use numerical quadrature formulas for Banach space valued functions in order to approximate semigroups that can be represented via the Hille-Phillips functional calculus. In particular, we find error estimates for our approximation method for the semigroup generated by the square root of a semigroup generator.

Date

2005

Document Availability at the Time of Submission

Release the entire work immediately for access worldwide.

Committee Chair

Frank Neubrander

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