Efficient Nordsieck second derivative general linear methods: construction and implementation

In this paper, by considering the order conditions for second derivative general linear methods of order p and stage order q=p-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q=p-1$$\end{document}, we investigate construction and implementation of these methods in the Nordsieck form with r=s+1=p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r=s+1=p$$\end{document}, where s and r are the number of internal and external stages of the method, respectively. Constructed methods are A- and L-stable which possess Runge–Kutta stability property. Some numerical experiments are provided in a variable stepsize environment to validate the efficiency of the constructed methods and reliability of the proposed error estimates.