Algorithmic Verification of Linearizability for Ordinary Differential Equations

Dmitry Lyakhov, Vladimir P. Gerdt, Dominik L. Michels

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Scopus citations

Abstract

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. The implementation of both algorithms is discussed and their application is illustrated using several examples.
Original languageEnglish (US)
Title of host publicationProceedings of the 2017 ACM on International Symposium on Symbolic and Algebraic Computation - ISSAC '17
PublisherAssociation for Computing Machinery (ACM)
Pages285-292
Number of pages8
ISBN (Print)9781450350648
DOIs
StatePublished - Jul 19 2017

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