Super implicit two-step collocation methods for ordinary differential equations

This paper introduces a class of two-step collocation methods for the numerical solution of ordinary differential equations. These methods which are equipped with the future point technique and described in two types, to approximate the solution in each step, use the numerical solution in some points in the two previous subintervals as well as in the future subinterval. The superior features of the proposed methods in convergence order and stability in comparison with the similar methods are analyzed. The achieved improvements are verified by giving some numerical experiments.