Solving Directly Second Order Initial Value Problems with Lucas Polynomial

Abstract

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]].