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dc.contributor.authorLyakhov, Dmitry
dc.contributor.authorGerdt, Vladimir P.
dc.contributor.authorMichels, Dominik L.
dc.date.accessioned2019-12-02T12:18:54Z
dc.date.available2019-12-02T12:18:54Z
dc.date.issued2019-07-15
dc.identifier.citationLyakhov, D. A., Gerdt, V. P., & Michels, D. L. (2020). On the algorithmic linearizability of nonlinear ordinary differential equations. Journal of Symbolic Computation, 98, 3–22. doi:10.1016/j.jsc.2019.07.004
dc.identifier.doi10.1016/j.jsc.2019.07.004
dc.identifier.urihttp://hdl.handle.net/10754/660360
dc.description.abstractSolving nonlinear ordinary differential equations is one of the fundamental and practically important research challenges in mathematics. However, the problem of their algorithmic linearizability so far remained unsolved. In this contribution, we propose a solution of this problem for a wide class of nonlinear ordinary differential equation of arbitrary order. We develop two algorithms to check if a nonlinear differential equation can be reduced to a linear one by a point transformation of the dependent and independent variables. In this regard, we have restricted ourselves to quasi-linear equations with a rational dependence on the occurring variables and to point transformations. While 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 our algorithms is discussed and evaluated using several examples.
dc.description.sponsorshipThe authors are grateful to Daniel Robertz and Greg Reid for helpful discussions and suggestions. This work has been partially supported by KAUST Baseline Funding (D. A. Lyakhov and D. L. Michels), by the RUDN University Program (5-100; V. P. Gerdt), and by Stanford University (D. L. Michels).
dc.publisherElsevier BV
dc.relation.urlhttps://linkinghub.elsevier.com/retrieve/pii/S0747717119300689
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Journal of Symbolic Computation. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Symbolic Computation, [[Volume], [Issue], (2019-07-15)] DOI: 10.1016/j.jsc.2019.07.004 . © 2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.titleOn the algorithmic linearizability of nonlinear ordinary differential equations
dc.typeArticle
dc.contributor.departmentVisual Computing Center (VCC)
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentComputer Science Program
dc.identifier.journalJournal of Symbolic Computation
dc.rights.embargodate2021-07-15
dc.eprint.versionPost-print
dc.contributor.institutionGroup of Algebraic and Quantum Computations, Joint Institute for Nuclear Research, Dubna, Russian Federation
dc.contributor.institutionPeoples' Friendship University of Russia (RUDN University), Moscow, Russian Federation
dc.contributor.institutionComputer Science Department, Stanford University, Stanford, CA, United States of America
kaust.personLyakhov, Dmitry
kaust.personMichels, Dominik L.
dc.date.published-online2019-07-15
dc.date.published-print2020-05


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