High order second derivative methods with Runge--Kutta stability for the numerical solution of stiff ODEs

Abstract

‎We describe the construction of second derivative general linear methods (SGLMs) of orders five and six‎. ‎We will aim for methods which are A--stable and have Runge--Kutta stability property‎. ‎Some numerical results are given to show the efficiency of the constructed methods in solving stiff initial value problems‎.