A Class of Multistep Method Containing Second Order Derivatives for Solving Stiff Ordinary Differential Equations

In this paper a general k-step k-order multistep method containing derivatives of second order is given. In particular, a class of k-step (k+1)th-order stiff stable multistep methods for k=3-9 is constructed. Under the same accuracy, these methods are possessed of a larger absolute stability region than those of Gear's [1] and Enright's [2]. Hence they are suitable for solving stiff initial value problems in ordinary differential equations.