Coordinate Basis Transformation Based Linearisation Method for Ordinary Differential Equations

DOI

10.2991/amms-17.2017.4How to use a DOI?

Keywords

coordinate basis; linearisation; Lie derivative

Abstract

In this paper, a linearisation method for nonlinear ordinary differential equations based on coordinate basis transformation is proposed. In order to transform a nonlinear equation into a linear one, we introduce a general framework to extract the coordinate basis of the differential system. Actually, by introducing a mapping function predefined, this extraction method could connect each state variable of the new system with the variables in the original one. Further, by using vector space for the closure of the Lie derivative, we can analytically obtain the mapping based on the subspace iteration. We argue that this method might be efficient in analyzing and solving ordinary differential systems of complex nonlinear forms.

Copyright

© 2017, 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  - Danlei Ye
AU  - Xin Jiang
AU  - Guanying Huo
AU  - Cheng Su
AU  - Zehong Lu
AU  - Bolun Wang
AU  - Zhiming Zheng
PY  - 2017/11
DA  - 2017/11
TI  - Coordinate Basis Transformation Based Linearisation Method for Ordinary Differential Equations
BT  - Proceedings of the 2017 International Conference on Applied Mathematics, Modeling and Simulation (AMMS 2017)
PB  - Atlantis Press
SP  - 14
EP  - 19
SN  - 1951-6851
UR  - https://doi.org/10.2991/amms-17.2017.4
DO  - 10.2991/amms-17.2017.4
ID  - Ye2017/11
ER  -