A new class of second derivative multistep‎ ‎methods for stiff ODEs

‎In this paper‎, ‎we study a new class of linear methods for the numerical solution of initial value‎ ‎problems in ordinary differential equations‎. ‎These methods have multivalue structure‎ ‎in which the second derivative of the solution together with a free parameter‎ ‎have been included‎. ‎Deriving the stability matrix‎ ‎of the methods and checking its eigenvalues‎, ‎we aim to fine the free parameter so that construct methods‎ ‎with better stability properties of high convergence order‎.