Algorithmic Verification of Linearizability for Ordinary Differential Equations

02/13/2017
by   Dmitry Lyakhov, et al.
0

For a nonlinear ordinary differential equation solved with respect to the highest order derivative and rational in the other derivatives and in the independent variable, we devise two algorithms to check if the equation can be reduced to a linear one by a point transformation of the dependent and independent variables. The first algorithm is based on a construction of the Lie point symmetry algebra and on the computation of its derived algebra. The second algorithm exploits the differential Thomas decomposition and allows not only to test the linearizability, but also to generate a system of nonlinear partial differential equations that determines the point transformation and the coefficients of the linearized equation. Both algorithms have been implemented in Maple and their application is illustrated using several examples.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
05/07/2021

ReLie: a Reduce program for Lie group analysis of differential equations

Lie symmetry analysis provides a general theoretical framework for inves...
research
02/04/2021

Certifying Differential Equation Solutions from Computer Algebra Systems in Isabelle/HOL

The Isabelle/HOL proof assistant has a powerful library for continuous a...
research
11/02/2022

Analysis and object oriented implementation of the Kovacic algorithm

This paper gives a detailed overview and a number of worked out examples...
research
10/23/2017

Algebra, coalgebra, and minimization in polynomial differential equations

We consider reasoning and minimization in systems of polynomial ordinary...
research
12/26/2015

Dynamic Computation of Runge Kutta Fourth Order Algorithm for First and Second Order Ordinary Differential Equation Using Java

Differential equations arise in mathematics, physics,medicine, pharmacol...
research
08/25/2020

Towards a noncommutative Picard-Vessiot theory

A Chen generating series, along a path and with respect to m differentia...

Please sign up or login with your details

Forgot password? Click here to reset