Solving Directly Second Order Initial Value Problems with Lucas Polynomial

Aims/ Objectives: This paper presents a one step hybrid numerical scheme with one o gridpoints 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 providesthe analysis of the scheme, while numerical implementation of the scheme and conclusion are inSections four and ve respectively.Methodology: The scheme is developed using collocation and interpolation technique invokedon Lucas polynomial.Results: The proposed scheme is consistent, zero stable and of order four and can estimate theapproximate solution at both step and o step points simultaneously by using variable step size.Conclusion: Numerical results are given to show the eciency of the proposed scheme over someexisting schemes of same and higher order[ [1],[2], [3],[4], [5], [6]].