Polynomial odes: examples, solutions, properties

  • Authors:

  • James S. Sochacki

  • Affiliations:

  • Department of Mathematics and Statistics, James Madison University, Harrisonburg, VA

  • Venue:
  • Neural, Parallel & Scientific Computations
  • Year:
  • 2010

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Abstract

Let P be a polynomial from Rn → Rn and D ∈ Rn. 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.