## 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 language | English (US) |
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Title of host publication | ISSAC 2017 - Proceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation |

Editors | Michael Burr |

Publisher | Association for Computing Machinery |

Pages | 285-292 |

Number of pages | 8 |

ISBN (Electronic) | 9781450350648 |

DOIs | |

State | Published - Jul 23 2017 |

Event | 42nd ACM International Symposium on Symbolic and Algebraic Computation, ISSAC 2017 - Kaiserslautern, Germany Duration: Jul 25 2017 → Jul 28 2017 |

### Publication series

Name | Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC |
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Volume | Part F129312 |

### Conference

Conference | 42nd ACM International Symposium on Symbolic and Algebraic Computation, ISSAC 2017 |
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Country/Territory | Germany |

City | Kaiserslautern |

Period | 07/25/17 → 07/28/17 |

### Bibliographical note

Publisher Copyright:© 2017 Association for Computing Machinery.

## Keywords

- Algorithmic linearization test
- Determining equations
- Differential Thomas decomposition
- Lie symmetry algebra
- Ordinary differential equations
- Point transformation
- Power series solutions

## ASJC Scopus subject areas

- General Mathematics