Numerical solution of damped forced oscillator problem using Haar wavelets

Document Type : Research Article


Department of Mathematics, Dr. B. R. Ambedkar National Institute of Technology, Jalandhar, Punjab-144011, India.


We present here the numerical solution of damped forced oscillator problem using Haar wavelet and compare the numerical results obtained with some well-known numerical methods such as Runge-Kutta fourth order classical and Taylor Series methods. Numerical results show that the present Haar wavelet method gives more accurate approximations than above said numerical methods.


1. Babolian, E. and Shahsawaran, A. Numerical solution of non-linear fredholm integral equations of the second kind using haar wavelets, J. Comput. Appl. Math. 225(2009) 87-95.
2. Cattani, C. Haar wavelet splines, J. Interdisciplinary Math. 4(2001) 35-47.
3. Chen, C.F. and Hsiao, C.H. Haar wavelet method for solving lumped and distributed-parameter systems, IEEE Proc.: Part D, 144(1) (1997) 87-94.
4. Haar, A. Zur theorie der orthogonalen Funktionsysteme, Math. Annal. 69(1910) 331-371.
5. Hariharan, G. and Kannan, K. An overview of Haar wavelet method for solving differential and integral equation, World Applied Sciences Journal 23(12) (2013) 1-14.
6. Hsiao, C.H. Wavelet approach to time-varying functional differential equations, Int. J. Computer Math. 87(3) (2008) 528-540.
7. Kouchi, M.R., Khosravi, M. and Bahmani, J. A numerical solution of Homogengous and Inhomogeneous Harmonic Differential equation with Haar wavelet, Int. J. Contemp. Math. Sciences 6(41) (2011) 2009-2018.
8. Lepik, U. Numerical solution of differential equations using Haar wavelets, Math. Comput. Simulat. 68 (2005) 127-143.
9. Lepik, U. Application of Haar wavelet transform to solving integral and differential equation, Proc. Estonian Acad. Sci. Phys. Math. 56(1) (2007) 28-46.
10. Lepik, U. Haar wavelet method for higher order differential equations, Int. J. MAth. Comput. 1 (2008) 84-94.
11. Lepik, U. Haar wavelet method for solving stiff differential equations, Math. Modeling and Analysis 4 (2009) 467-489.
12. Lepik, U. Solution of optimal control problems via Haar wavelets, Int. J.
Pure. Appl. Math. 55 (2009) 81-94.
13. Ohkita, M. and Kobayashi, Y. An application of rationalized Haar functions to solution of linear differential equations, IEEE Trans. Circuit System 9 (2003) 853-862.
14. Rama, B.B. and Dukkipati, V. Advanced dynamics, Alpha Science, Pangbourne, 2001.
15. Razzaghi, M. and Ordokhani,Y. An application of rationalized Haar functions for variational problems, Appl. MAth. Comput. 122 (2001) 353-364.
16. Saeed, U. and Rehman, M.U. Haar wavelet operational matrix method for fractional oscillation equations, International Journal of Mathematics and Mathematical Sciences, (2014) 1-8.
17. Simmons, G.F. Differential equations with applications and historical notes, Mcgraw-Hill, London. 1972.
18. Sunmonu, A. Implementation of wavelet solution to second order differential equations with maple, Applied Mathematical Sciences 6(127) (2012) 6311-6326.
19. Thomsen, J.J. Vibrations and stability order and chaos, Mc-graw-Hill, London, 1997.