Numerical Simulation of the Harmonic Oscillator Differential Equation Using Finite Difference Schemes

  • Lukman O. Salaudeen Federal University Oye-ekiti
  • Abraham A. Obayomi Ekiti State University, Ado-ekiti
  • Yidiat O Aderinto University of Ilorin
Keywords: Finite Difference, Interpolant, Harmonic Oscillator, Consistent.


In this study, we have developed a new type of finite difference scheme using dynamically renormalized denominator functions and trigonometric and exponential interpolating functions. These schemes show local stability, convergence, and consistency. The model provides an improved numerical scheme for the Harmonic Oscillator Differential Equation. Additionally, we compared the new model with a previous discrete model for the Harmonic equation and also confirmed the suitability of the new schemes for the numerical simulation of the tested problems.  

Author Biographies

Abraham A. Obayomi, Ekiti State University, Ado-ekiti
Department of Mathematics
Yidiat O Aderinto, University of Ilorin
Department of Mathematics (Professor)


Alharthi, M. S. (2023). Wave solitons to a nonlinear doubly dispersive equation in describing the nonlinear wave propagation via two analytical techniques. Results in Physics, 47, 106362.

Anguelov, R. and Lubuma. H. (2003). Nonstandard finite difference method by nonlocal approximation, Mathematics and Computers in simulation, 6: 465-475.

Dalquist, G. (1978). On accuracy and unconditional stability of Linear Equations, BIT, 18: 133-136.

Darley, O. G., Adenowo, A. A. and Yussuff, A. I. (2021). Finite Difference Numerical Method: Applications in lightning electromagnetic pulse and heat diffusion, FUOYE Journal of Engineering and Technology, 6(3): 27-33.

Fatunla S. O. (1998). Numerical Methods for Initial Values Problems on Ordinary Differential Equations, Academic Press, New York.

Henrici P. (1962). Discrete Variable Methods in ODE”, John Willey & Sons, New York.

Jain, V.K., Behera, B.K. & Panigrahi, P.K. (2021). Quantum simulation of discretized harmonic oscillator. Quantum Stud.: Math. Found. 8, 375–390.

Mickens R.E. (1981). Nonlinear Oscillations, Cambridge University Press, New York.

Mickens R. E. (1994). Non-standard Finite Difference Models of Differential Equations, World Scientific, Singapore, 115: 144-162,1994.

Obayomi A.A. and Oke M.O. (2016). Development of new Nonstandard denominator function for Finite Difference schemes, Journal of the Nigerian Association of Mathematical Physics, 33(1): 50-60, 2016.

Obayomi A A. (2018). Development of a discrete model for the Tsunami Tidal Waves, Journal of Maths and Computer Science J. Math. Comput. Sci., 8(1): 98-113.

Salehi, M. & Granpayeh, N. (2020). Numerical solution of the Schrödinger equation in polar coordinates using the finite-difference time-domain method. J Comput Electron, 19: 91–102.

Sprott, J. C., & Hoover, W. G. (2017). Harmonic oscillators with nonlinear damping. International Journal of Bifurcation and Chaos, 27(11), 1730037.