@article{kan-ois-99-aa-ode-tr,
  author = {Yuchi Kanzawa and {Shin'ichi} Oishi},
  title = {A Numerical Method to Prove the Existence of Solutions for Nonlinear {ODEs} Using Affine Arithmetic},
  journal = {IEICE Technical Report},
  publisher = {Institute of Electronics, Information and Communication Engineers},
  volume = {99},
  number = {42},
  pages = {39-44},
  year = 1999,
  month = may,
  note = {See also~\cite{kan-ois-02-aa-ode}},
  abstract = {In this paper, we shall propose a method to prove the existence of the solutions for nonlinear ordinary differential equa tions using affine arithmetic instead of using interval arithmetic. In the case using interval arithmetic, we must use Krawczyk-like operator, which is the mean value form for Newton operator,because of the disadvantage of interval arithmetic. Otherwise, we use affine arithmetic to Newton operator directly since affine arithmetic is effective to variables-dependent calculations. In other words, we need not Mean value theorem any more.}
}