On Expansion of a Solution of General Non-autonomous Polynomial Differential Equation
Classical Analysis and ODEs
2014-03-31 v1
Abstract
We give a recursive formula for an expansion of a solution of a general non-autonomous polynomial differential equation. The formula is given on the algebraic level with a use of shuffle product. This approach minimizes the number of integrations on each order of expansion. Using combinatorics of trees we estimate the radius of convergence of the expansion.
Keywords
Cite
@article{arxiv.1403.7460,
title = {On Expansion of a Solution of General Non-autonomous Polynomial Differential Equation},
author = {Gabriel Pietrzkowski},
journal= {arXiv preprint arXiv:1403.7460},
year = {2014}
}
Comments
13 pages, To be published in Journal of Dynamical and Control Systems