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Journal of Scientific Computing

Erschienen in:

30.11.2017

A Note on High-Precision Approximation of Asymptotically Decaying Solution and Orthogonal Decomposition

verfasst von: John Nicponski, Jae-Hun Jung

Erschienen in: Journal of Scientific Computing | Ausgabe 1/2018

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Abstract

In some physical applications, the decaying rate of asymptotically decaying solution is more important than the solution magnitude itself in understanding the physical system such as the late-time behavior of decaying fields in black hole space-time. In Khanna (J Sci Comput 56(2):366–380, 2013), it was emphasized that high-precision arithmetic and high-order methods are required to capture numerically the correct decaying rate of the late-time radiative tails of black-hole system in order to prevent roundoff errors from inducing a wrong power-law decay rate in the numerical approximation. In this paper, we explain how roundoff errors induce a wrong decay mode in the numerical approximation using simple linear differential equations. Then we describe the orthogonal decomposition method as a possible technique to remove wrong decaying modes induced by roundoff errors in the numerical approximation.

Vorheriger Artikel A Spectral Collocation Method for Nonlinear Fractional Boundary Value Problems with a Caputo Derivative

Nächster Artikel Comparison of Some Entropy Conservative Numerical Fluxes for the Euler Equations

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Titel: A Note on High-Precision Approximation of Asymptotically Decaying Solution and Orthogonal Decomposition
verfasst von: John Nicponski
Jae-Hun Jung
Publikationsdatum: 30.11.2017
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 1/2018
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-017-0619-0

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