M EGBALJOO - Faculty of Mathematics, Statistics and Computer Science, University of Tabriz, Tabriz, Iran
G HOJJATI - Faculty of Mathematics, Statistics and Computer Science, University of Tabriz, Tabriz, Iran

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

Initial value problem, Second derivative methods, Stability, Stiff systems.