Geodesic
Cauchy-Kowalevski and polynomial ordinary differential equations
Electronic Journal of Differential Equations, Tome 2012 (2012).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 34A12, 34A34, 35A10
Keywords: automatic differentiation, power series, Taylor series, polynomial ODE, majorant, error bound 
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     author = {Thelwell, Roger J. and Warne, Paul G. and Warne, Debra A.},
     title = {Cauchy-Kowalevski and polynomial ordinary differential equations},
     journal = {Electronic Journal of Differential Equations},
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     volume = {2012},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a36/}
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Thelwell, Roger J.; Warne, Paul G.; Warne, Debra A. Cauchy-Kowalevski and polynomial ordinary differential equations. Electronic Journal of Differential Equations, Tome 2012 (2012). http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a36/