A note on high-precision approximation of asymptotically decaying solution and orthogonal decomposition
SCIE
SCOPUS
- Title
- A note on high-precision approximation of asymptotically decaying solution and orthogonal decomposition
- Authors
- JUNG, JAE HUN; Nicponski, John
- Date Issued
- 2018-07
- Publisher
- Springer
- 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.
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/105750
- DOI
- 10.1007/s10915-017-0619-0
- ISSN
- 0885-7474
- Article Type
- Article
- Citation
- Journal of Scientific Computing, vol. 76, no. 1, page. 189 - 215, 2018-07
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