A New Approach to Obtain Infinitesimal Generators of Lie Symmetry Group of ODEs

Lie’s theory of symmetry groups of differential equations plays an important role to analyse and solve differential equations, for instance by decreasing the order of equation. There are some analytic methods to find the infinitesimal generators that span the Lie algebra of symmetries. In this paper, we convert the problem of finding infinitesimal generators to the problem of solving a system of polynomial equations in the context of computational algebraic geometry, and then we use Gröbner basis as a novel computational tool to solve this problem.