An L-stable extended two-step method for the integration of ordinary differential equations

A class of linear multistep methods (LMMs) for the numerical solution of first-order differential and stiff differential equations are considered. The accuracy and stability properties of these methods are investigated. By judicious choice of the coefficients in these formulae a method is derived which is the new method which is shown to be L-stable and so is appropriate for the solution of certain ordinary differential and stiff differential equations. Numerical results are presented for several test problems.