Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 11, pp. 1-8.

Title: Cauchy-Kowalevski and polynomial ordinary differential equations

Authors: Roger J. Thelwell (James Madison Univ., Harrisonburg, VA, USA)
         Paul G. Warne  (James Madison Univ., Harrisonburg, VA, USA)
	 Debra A. Warne (James Madison Univ., Harrisonburg, VA, USA)

Abstract:
 The Cauchy-Kowalevski Theorem is the foremost result guaranteeing
 existence and uniqueness of local solutions for analytic
 quasilinear partial  differential equations with Cauchy initial data.
 The techniques of Cauchy-Kowalevski may also be applied to
 initial-value ordinary differential equations.
 These  techniques, when applied in the polynomial ordinary
 differential equation setting, lead one naturally to a method
 in which coefficients of the series solution are easily
 computed in a recursive manner, and an explicit majorization
 admits a clear a priori error bound.
 The error bound depends only on immediately
 observable quantities of the polynomial system; coefficients,
 initial conditions, and polynomial degree.
 The numerous benefits of the polynomial system are shown for
 a specific example.
 
Submitted October 11, 2010. Published January 17, 2012.
Math Subject Classifications: 34A12, 34A34, 35A10.
Key Words: Automatic differentiation; power series; Taylor series;
           polynomial ODE; majorant; error bound.