Solving Directly Second Order Initial Value Problems with Lucas Polynomial

Aims/ Objectives: This paper presents a one step hybrid numerical scheme with one off grid points for solving directly the general second order initial value problems.
Study Design: Section one which is the introduction, give a brief about initial value problem. In the next section derivation of one step hybrid scheme is considered. Section Three provides the analysis of the scheme, while numerical implementation of the scheme and conclusion are in Sections four and five respectively.
Methodology: The scheme is developed using collocation and interpolation technique invoked on Lucas polynomial.
Results: The proposed scheme is consistent, zero stable and of order four and can estimate the approximate solution at both step and o step points simultaneously by using variable step size.
Conclusion: Numerical results are given to show the efficiency of the proposed scheme over some existing schemes of same and higher order[ [1],[2], [3],[4], [5], [6]].