Coordinate Basis Transformation Based Linearisation Method for Ordinary Differential Equations

摘要

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.