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)|
|Title of host publication||Proceedings of the 2017 ACM on International Symposium on Symbolic and Algebraic Computation - ISSAC '17|
|Publisher||Association for Computing Machinery (ACM)|
|Number of pages||8|
|State||Published - Jul 19 2017|