Special extended Nyström tree theory for ERKN methods

• Autores: Xiong You, Yonglei Fang, Jinxi Zhao
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 263, Nº 1, 2014, págs. 478-499
• Idioma: inglés
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• Resumen

  • 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.