Resumen de Special extended Nyström tree theory for ERKN methods

Xiong You, Yonglei Fang, Jinxi Zhao

• The aim of this paper is to develop a unified special extended Nyström tree (SEN-tree) theory which provides a theoretical framework for the order conditions of multidimensional extended Runge�Kutta�Nyström (ERKN) methods proposed by X. Wu et al. (Wu et al., 2010). The new SEN tree theory is complete and consistent, which has overcome the drawback of the bi-coloured tree theory in H. Yang et al.�s work (Yang et al., 2009) where two ��branch sets�� have to be constructed for the true solutions and for the numerical solutions, respectively.