Block Second Derivative Methods for the Direct Solution of Second Order Initial Value Problems of (ODEs) Using Lucas Polynomials as Basis Function

This paper presents a self - starting block method for the direct solution of general second order initial value problems of ordinary differential equations. The method was developed via interpolation and collocation of the Lucas polynomial as basis function. A continuous linear multistep method was generated and was evaluated at some desired points to give the discrete block method. The block method was investigated and was found to be consistent, zero stable and convergent. The method was applied on some second order initial value problems of ordinary differential equations and the performance was relatively better than those constructed by Awari et al and Jator et al respectively.