Sequential second derivative general linear methods for stiff systems

Abstract

‎Second derivative general linear methods (SGLMs) as an extension‎ <br />‎of general linear methods (GLMs) have been introduced to improve‎ <br />‎the stability and accuracy properties of GLMs‎. ‎The coefficients of‎ <br />‎SGLMs are given by six matrices‎, ‎instead of four matrices for‎ <br />‎GLMs‎, ‎which are obtained by solving nonlinear systems of order and‎ <br />‎usually Runge--Kutta stability conditions‎. ‎In this paper‎, ‎we‎ <br />‎introduce a technique for construction of an special case of SGLMs‎ <br />‎which decreases the complexity of finding coefficients matrices‎.