Special extended Nyström tree theory for ERKN methods

作者：

Highlights：

• A systematic and uniform special extended Nyström tree (SEN-tree) theory.

• Order conditions for extended Runge–Kutta–Nyström (ERKN) methods.

• New simplifying assumptions for the coefficients of ERKN methods.

• Practical ERKN schemes with numerical illustrations.

摘要

•A systematic and uniform special extended Nyström tree (SEN-tree) theory.•Order conditions for extended Runge–Kutta–Nyström (ERKN) methods.•New simplifying assumptions for the coefficients of ERKN methods.•Practical ERKN schemes with numerical illustrations.

论文关键词：primary,65L05,65L06,65M20,65N40,65R20,Special extended Nyström trees,Second-order oscillatory problems,Extended Runge–Kutta–Nyström methods,Order conditions

论文评审过程：Received 22 August 2012, Revised 17 September 2013, Available online 9 January 2014.

论文官网地址：https://doi.org/10.1016/j.cam.2013.12.043