An improved Fixed Step-size Adams Method Based On Taylor Extrapolation

DOI

10.2991/mce-14.2014.164How to use a DOI?

Keywords

Taylor extrapolation; fixed-step; computational accuracy; truncation error; linear combinations

Abstract

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 .

Copyright

© 2014, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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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  - Proceedings of the 2014 International Conference on Mechatronics, Control and Electronic Engineering
PB  - Atlantis Press
SP  - 730
EP  - 733
SN  - 1951-6851
UR  - https://doi.org/10.2991/mce-14.2014.164
DO  - 10.2991/mce-14.2014.164
ID  - He2014/03
ER  -