Contact Linearizability of Scalar Ordinary Differential Equations of Arbitrary Order
KAUST DepartmentVisual Computing Center, King Abdullah University of Science and Technology, Al-Khawarizmi Bldg 1, Thuwal, 23955-6900, Kingdom of Saudi Arabia
Visual Computing Center (VCC)
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Computer Science Program
Embargo End Date2021-12-02
Permanent link to this recordhttp://hdl.handle.net/10754/666227
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AbstractWe 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.
CitationLiu, Y., Lyakhov, D., & Michels, D. L. (2020). Contact Linearizability of Scalar Ordinary Differential Equations of Arbitrary Order. Lecture Notes in Computer Science, 421–430. doi:10.1007/978-3-030-60026-6_24
SponsorsThis work has been funded by the King Abdullah University of Science and Technology (KAUST baseline funding). The authors are grateful to Peter Olver for helpful discussions and to the anonymous reviewers for comments that led to improvement of the paper.
Conference/Event name22nd International Workshop on Computer Algebra in Scientific Computing, CASC 2020