%0 Journal Article
%T Cauchy-Kowalevski and polynomial ordinary differential equations
%A Roger J. Thelwell
%A Paul G. Warne
%A Debra A. Warne
%J Electronic Journal of Differential Equations
%D 2012
%I Texas State University
%X 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.
%K Automatic differentiation
%K power series
%K Taylor series
%K polynomial ODE
%K majorant
%K error bound
%U http://ejde.math.txstate.edu/Volumes/2012/11/abstr.html