Contact Linearizability of Scalar Ordinary Differential Equations of Arbitrary Order

Yang Liu, Dmitry Lyakhov, Dominik L. Michels

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


We consider the problem of the exact linearization of scalar nonlinear ordinary differential equations by contact transformations. This contribution is extending the previous work by Lyakhov, Gerdt, and Michels addressing linearizability by means of point transformations. We have restricted ourselves to quasi-linear equations solved for the highest derivative with a rational dependence on the occurring variables. As in the case of point transformations, our algorithm is based on simple operations on Lie algebras such as computing the derived algebra and the dimension of the symmetry algebra. The linearization test is an efficient algorithmic procedure while finding the linearization transformation requires the computation of at least one solution of the corresponding system of the Bluman-Kumei equation.
Original languageEnglish (US)
Title of host publicationComputer Algebra in Scientific Computing
PublisherSpringer Nature
Number of pages10
ISBN (Print)9783030600259
StatePublished - Oct 2 2020


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