Polynomial odes: examples, solutions, properties

ABSTRACT. Let P be a polynomial from R → R and D ∈ R. I will consider the properties of the class of ODEs Y ′ = P (y) ; Y (0) = D and their solutions. The solution space to these ODEs form a proper subspace of the analytic functions with ODEs. They have many interesting algebraic and topological properties. I will present efficient methods for generating the power series solutions to these polynomial initial value ODEs. These methods give a priori error estimates that are optimal in the class of polynomial ODEs. Examples showing the power of these theorems are presented, including Newton’s N-Body problem. AMS (MOS) Subject Classification. 49K15.