Second derivative GLM with nearly ARK stability

Abstract This paper considers a special subclass of second derivative general linear methods (SD-GLM). This new class of methods will be known as the second derivative GLMwith nearly almost Runge-Kutta stability (SD-NARK-stability). It is one of the possible generalization of the classical second derivative Runge-Kutta method (SD-RKM) suitable for the solution of non-stiff initial value problems (IVPs) in ordinary differential equations (ODEs).