Algebraic conditions for high-order convergent deferred correction schemes based on Runge-Kutta-Nyström methods for second order boundary value problems

Authors:
M. Van Daele;T. Van Hecke
Affiliations:
Vakgroep Toegepaste Wiskunde en Informatica, Universiteit Gent, Krijgslaan 281-S9, B9000 Gent, Belgium;Hogeschool Gent, Schoonmeersstraat 52, B9000 Gent, Belgium
Venue:
Applied Numerical Mathematics
Year:
2002

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Abstract

In [T. Van Hecke, M. Van Daele, J. Comp. Appl. Math. 132 (2001) 107-125] the investigation of high-order convergence of deferred correction schemes for the numerical solution of second order nonlinear two-point boundary value problems not containing the first derivative, is made. The derivation of the algebraic conditions to raise the increase of order by the deferred correction scheme was based on Taylor series expansions. In this paper we describe a more elegant way by means of P-series to obtain this necessary conditions and generalize this idea to equations of the form y'' = f(t, y, y').