document: Algebraic conditions for high-order convergent deferred correction schemes based on Runge-Kutta-Nystrom methods for second order boundary value problems In -LSB- T. Van Hecke , M. Van Daele , J. Comp . Appl . Math. , vol . 132 , p. 107-125 , -LRB- 2001 -RRB- -RSB- 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 -LRB- t , y , y ' -RRB-
doc_bio_tags: B I O O O B I I O O O O O B I I I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
extractive_keyphrases: second order boundary value problems deferred correction schemes algebraic conditions taylor series expansions
abstractive_keyphrases: high-order convergent deferred correction schemes runge-kutta-nystrom methods second order nonlinear two-point boundary value problems