Symmetric collocation ERKN methods for general second-order oscillators

Abstract

For the numerical solution of the general second-order oscillatory system $$y''+ M y = f(y,y')$$, You et al. (Numer Algorithm 66:147–176, 2014) proposed the extended Runge–Kutta–Nystrom (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 experiments show the high effectiveness of the new ERKN methods compared to their RKN counterparts.