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For the numerical solution of the general second-order oscillatory system $$y''+ M y = f(y,y')$$ y′′+My=f(y,y′) , You et al. (Numer Algorithm 66:147–176, 2014) proposed the extended Runge–Kutta–Nyström (ERKN) methods. This paper is devoted to symmetric collocation ERKN methods of Gauss and Lobatto IIIA types by Lagrange interpolation. Linear stability of the new ERKN methods is analyzed. Numerical...
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...
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