A new type OF hybrid multistep multiderivative formula for solving stiff IVPs

We present a new class of higher-order multistep multiderivative methods for the numerical solution of stiff initial value problems. These methods are obtained based on free parameters and off-point. The methods have minimum error bounds. The constructed class is A-stable for orders 3 and 4, and A(α)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$A(\alpha)$\end{document}-stable for orders 5 and 6. The new class is L-stable for all orders. They are suitable for solving stiff systems of initial value problems with large eigenvalues lying close to the imaginary axis. The stability regions of the new class are plotted, and some problems are solved, which show the superiority of the class in efficiency and accuracy.