RELIABILITY OF NUMERICAL SOLUTIONS OF THE G-EULER PROCESSRELIABILITY OF NUMERICAL SOLUTIONS OF THE G-EULER PROCESS
- Authors
- Dong Won Yu
- Issue Date
- Jan-2022
- Publisher
- 한국산업응용수학회
- Keywords
- G-Euler process; Scalar skew-symmetric matrix; Maximum step size; Zero point; Zero region; Match rate.
- Citation
- Journal of the Korean Society for Industrial and Applied Mathematics, v.26, no.1, pp 49 - 66
- Pages
- 18
- Journal Title
- Journal of the Korean Society for Industrial and Applied Mathematics
- Volume
- 26
- Number
- 1
- Start Page
- 49
- End Page
- 66
- URI
- https://scholarworks.bwise.kr/cau/handle/2019.sw.cau/61733
- DOI
- 10.12941/jksiam.2022.26.049
- ISSN
- 1226-9433
1229-0645
- Abstract
- The G-Euler process has been proposed to overcome the difficulties of the cal culation of the exponential function of the Jacobian. It is an explicit method that uses the exponential function of the scalar skew-symmetric matrix. We define the moving shapes of true solutions and the moving shapes of numerical solutions. It is discussed whether the moving shape of the numerical solution matches the moving shape of the true solution. The match rates of these two kinds of moving shapes are sequentially calculated by the G-Euler process without using the true solution. It is shown that the closer the minimum match rate is to 100%, the more closely the numerical solutions follow the true solutions to the end. The minimum match rate indicates the reliability of the numerical solution calculated by the G-Euler process. The graphs of the Lorenz system in Perko [1] are different from those drawn by the G-Euler process. By the way, there is no basis for claiming that the Perko’s graphs are reliable.
- Files in This Item
- There are no files associated with this item.
- Appears in
Collections - College of Natural Sciences > Department of Mathematics > 1. Journal Articles
![qrcode](https://api.qrserver.com/v1/create-qr-code/?size=55x55&data=https://scholarworks.bwise.kr/cau/handle/2019.sw.cau/61733)
Items in ScholarWorks are protected by copyright, with all rights reserved, unless otherwise indicated.