Rational inversion of the Laplace transform

Document Type

Article

Publication Title

Journal of Evolution Equations

Publication Date

6-1-2012

Abstract

This paper studies new inversion methods for the Laplace transform of vector-valued functions arising from a combination of A-stable rational approximation schemes to the exponential and the shift operator semigroup. Each inversion method is provided in the form of a (finite) linear combination of the Laplace transform of the function and a finite amount of its derivatives. Seven explicit methods arising from A-stable schemes are provided, such as the Backward Euler, RadauIIA, Crank-Nicolson, and Calahan scheme. The main result shows that, if a function has an analytic extension to a sector containing the nonnegative real line, then the error estimate for each method is uniform in time. © 2012 Springer Basel AG (outside the USA).

Volume

12

Issue

2

First Page

435

Last Page

457

DOI

10.1007/s00028-012-0139-1

ISSN

14243199

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