An Error Embedded Runge-Kutta Method for Initial Value Problems
- Authors
- Bu, Sunyoung; Jung, WonKyu; Kim, Philsu
- Issue Date
- Jun-2016
- Publisher
- KYUNGPOOK NATL UNIV, DEPT MATHEMATICS
- Keywords
- Error embedded Runge-Kutta method; Embedded Runge-Kutta method; Initial value problem
- Citation
- KYUNGPOOK MATHEMATICAL JOURNAL, v.56, no.2, pp.311 - 327
- Journal Title
- KYUNGPOOK MATHEMATICAL JOURNAL
- Volume
- 56
- Number
- 2
- Start Page
- 311
- End Page
- 327
- URI
- https://scholarworks.bwise.kr/hongik/handle/2020.sw.hongik/7751
- DOI
- 10.5666/KMJ.2016.56.2.311
- ISSN
- 1225-6951
- Abstract
- In this paper, we propose an error embedded Runge-Kutta method to improve the traditional embedded Runge-Kutta method. The proposed scheme can be applied into most explicit embedded Runge-Kutta methods. At each integration step, the proposed method is comprised of two equations for the solution and the error, respectively. These solution and error are obtained by solving an initial value problem whose solution has the information of the error at each integration step. The constructed algorithm controls both the error and the time step size simultaneously and possesses a good performance in the computational cost compared to the original method. For the assessment of the effectiveness, the van der Pol equation and another one having a difficulty for the global error control are numerically solved. Finally, a two-body Kepler problem is also used to assess the efficiency of the proposed algorithm.
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- Appears in
Collections - College of Science and Technology > Department of Computer and Information Communications Engineering > 1. Journal Articles
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