AN EFFICIENT DIRECT COLLOCATION METHOD FOR THE INTEGRATION OF GENERAL SECOND ORDER INITIAL VALUE PROBLEMS

In this paper we present a direct method for the integration of Second order initial value problem without first reducing them to a system of first orders. New two-step finite difference collocation methods of orders two and four were derived. These first derivative approximations were combined with the Numerov method for a direct application to the general second order initial value problem for ordinary differential equations. Two classical problems in literature were considered and the results compared. The proposed method is more efficient approach for direct integration process and an option for a continuous output.