An improved Fixed Step-size Adams Method Based On Taylor Extrapolation
Ai-lin He, Kai Xu, Hailiang Yang, Kai Bao
Available Online March 2014.
- https://doi.org/10.2991/mce-14.2014.164How to use a DOI?
- Taylor extrapolation; fixed-step; computational accuracy; truncation error; linear combinations
- As to the numerical solution of ordinary differential equations, this paper introduces a new technique to improve the precision of the PECE form of the Adams method, which calculates the estimation of the local truncation error in every single integral step by using Taylor extrapolation. Through proper linear combinations of predicted value and corrected value, the most of the truncation error will be diminished. Moreover, a detailed theoretical derivation is also proposed, and the general laws of the integration equations’ coefficients with different orders are given in tabular form, which facilitates the engineering practice. Finally, specific single differential equation and satellite orbit two-body motion equations are taken as examples to test this improved method, and stimulation results indicates that the improved Adams method can achieve a higher computational accuracy, nearly one order of magnitude, when compared with the unimproved method, which proves the effectiveness and efficiency of our proposed method .
- Open Access
- This is an open access article distributed under the CC BY-NC license.
Cite this article
TY - CONF AU - Ai-lin He AU - Kai Xu AU - Hailiang Yang AU - Kai Bao PY - 2014/03 DA - 2014/03 TI - An improved Fixed Step-size Adams Method Based On Taylor Extrapolation BT - 2014 International Conference on Mechatronics, Control and Electronic Engineering (MCE-14) PB - Atlantis Press SP - 730 EP - 733 SN - 1951-6851 UR - https://doi.org/10.2991/mce-14.2014.164 DO - https://doi.org/10.2991/mce-14.2014.164 ID - He2014/03 ER -