Some new multistep methods for solving ordinary differential equations

Three sets of linear multistep formulae for solving stiff and nonstiff ordinary differential equations are presented. Two of the sets are based on Adams-Moulton and stiff formulae used by Gear [19691. A third set of formulae based on least-squares approximation is shown to be stiffly-stable up to order 8 and is suitable for solving stiff differential equations.