Algorithmic Verification of Linearizability for Ordinary Differential Equations
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AbstractFor 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.
CitationLyakhov DA, Gerdt VP, Michels DL (2017) Algorithmic Verification of Linearizability for Ordinary Differential Equations. Proceedings of the 2017 ACM on International Symposium on Symbolic and Algebraic Computation - ISSAC ’17. Available: http://dx.doi.org/10.1145/3087604.3087626.
SponsorsThe authors are grateful to Daniel Robertz and Boris Dubrov for helpful discussions and to the anonymous reviewers for several insightful comments that led to a substantial improvement of the paper. This work has been partially supported by the King Abdullah University of Science and Technology (KAUST baseline funding; D. A. Lyakhov and D. L. Michels), by the Russian Foundation for Basic Research (grant No.16-01-00080; V. P. Gerdt), and by the Ministry of Education and Science of the Russian Federation (agreement 02.a03.21.0008; V. P. Gerdt).
JournalProceedings of the 2017 ACM on International Symposium on Symbolic and Algebraic Computation - ISSAC '17
Conference/Event name42nd ACM International Symposium on Symbolic and Algebraic Computation, ISSAC 2017