Numerical Solutions of the Harmonic Oscillators using Adomian Decomposition Method

S. Sekar; A. Kavitha

doi:https://doi.org/10.14445/22315373/IJMTT-V24P508

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 24 | Number 1 | Year 2015 | Article Id. IJMTT-V24P508 | DOI : https://doi.org/10.14445/22315373/IJMTT-V24P508

Numerical Solutions of the Harmonic Oscillators using Adomian Decomposition Method

S. Sekar, A. Kavitha

Abstract

In this article, the Adomian Decomposition Method (ADM) is used to study the harmonic oscillators [6]. The obtained discrete solutions using ADM are compared with the Runge- Kutta (RK) method, Single-term Haar wavelet series (STHW) and ODE45 solutions of the harmonic oscillators and are found to be very accurate. Solution and Error graphs for discrete and exact solutions are presented in a graphical form to show efficiency of this method. This ADM can be easily implemented in a digital computer and the solution can be obtained for any length of time.

Keywords

Harmonic oscillators, ODE45 in Matlab, Runge-Kutta method, Single-term Haar wavelet series.

References

[1] G. Adomian, “Solving Frontier Problems of Physics: Decomposition method”, Kluwer, Boston, MA, 1994.
[2] Blanchard, Olivier and Charles Kahn, “The Solution of Linear Difference Models under Rational Expectations,” Econometrica 45, July 1985, pp. 1305-1311.
[3] J. C. Butcher, “The Numerical Methods for Ordinary Differential Equations”, 2003, John Wiley & Sons, U.K.
[4] S. Sekar and A. Kavitha, “Numerical Investigation of the Time Invariant Optimal Control of Singular Systems Using Adomian Decomposition Method”, Applied Mathematical Sciences, vol. 8, no. 121, pp. 6011-6018, 2014.
[5] S. Sekar and A. Kavitha, “Analysis of the linear timeinvariant Electronic Circuit using Adomian Decomposition Method”, Global Journal of Pure and Applied Mathematics, vol. 11, no. 1, pp. 10-13, 2015.
[6] S. Sekar, A. Manonmani and E. Paramanathan, “Numerical Strategy of the Harmonic oscillators using single-term Haar wavelet series”, Elixir Applied Mathematics online Journal, vol. 38, pp. 4228-4231, 2011.
[7] S. Sekar and M. Nalini, “Numerical Analysis of Different Second Order Systems Using Adomian Decomposition Method”, Applied Mathematical Sciences, vol. 8, no. 77, pp. 3825-3832, 2014.
[8] S. Sekar and M. Nalini, “Numerical Investigation of Higher Order Nonlinear Problem in the Calculus of Variations Using Adomian Decomposition Method”, IOSR Journal of Mathematics, vol. 11, no. 1 Ver. II, (Jan-Feb. 2015), pp. 74- 77.
[9] S. Sekar and M. Nalini, “A Study on linear time-invariant Transistor Circuit using Adomian Decomposition Method”, Global Journal of Pure and Applied Mathematics, vol. 11, no. 1, pp. 1-3, 2015.

Citation :

S. Sekar, A. Kavitha, "Numerical Solutions of the Harmonic Oscillators using Adomian Decomposition Method," International Journal of Mathematics Trends and Technology (IJMTT), vol. 24, no. 1, pp. 64-66, 2015. Crossref, https://doi.org/10.14445/22315373/IJMTT-V24P508