Doctor of Philosophy (PhD)
In this dissertation, we introduce Post-Widder-type inversion methods for the Laplace transform based on A-stable rational approximations of the exponential function. Since the results hold for Banach-space-valued functions, they yield efficient time-discretization methods for evolution equations of convolution type; e.g., linear first and higher order abstract Cauchy problems, inhomogeneous Cauchy problems, delay equations, Volterra and integro-differential equations, and problems that can be re-written as an abstract Cauchy problem on an appropriate state space.
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Ozer, Koray, "Laplace Transform Inversion and Time-Discretization Methods for Evolution Equations" (2008). LSU Doctoral Dissertations. 3710.