Stable Runge–Kutta–Nyström methods for dissipative stiff problems

The definition of stability for Runge–Kutta–Nyström methods applied to stiff second-order in time problems has been recently revised, proving that it is necessary to add a new condition on the coefficients in order to guarantee the stability. In this paper, we study the case of second-order in time problems in the nonconservative case. For this, we construct an \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$R$\end{document}-stable Runge–Kutta–Nyström method with two stages satisfying this condition of stability and we show numerically the advantages of this new method.