Two Step Finite Difference Scheme For The Numerical Solution Of Second Order Ordinary Differential Equations Arising From Dynamical Systems
Adesoji Abraham OBAYOMI
Department of Mathematics, Ekiti State University, Ado – Ekiti, Nigeria.
Michael Olufemi OKE
Department of Mathematics, Ekiti State University, Ado – Ekiti, Nigeria.
Samuel Olukayode AYINDE
Department of Mathematics, Ekiti State University, Ado – Ekiti, Nigeria.
Adewale Emmanuel ADENIPEKUN
Department of Statistics, Federal Polytechnic, Ede, Osun State, Nigeria.
Olu Sunday ADETOLAJU
Department of Computer Science, Ekiti State University, Ado – Ekiti, Nigeria.
Keywords: Non-standard method, Hybrid, Interpolation function, Standard finite difference method, Dynamical model
Abstract
This paper presents a new set of two step finite difference scheme for the numerical solution of some initial value second order ordinary differential equations arising from dynamical systems. We applied a combination of non-standard transformation of the differential components and an interpolation function to create a new simulation model that can be used to approximate the dynamics of a physical phenomenon whose state equations can be represented by second order ordinary differential equations. The resulting scheme have been applied to some initial value problems and has been shown to be very suitable to a class of second order ordinary differential equations with vanishing velocity components. The schemes have been found to possess desirable qualitative properties and it converges to the analytical solution.