Comparing Numerical Methods for the Solution of the Damped Forced Oscillator Problem
الموضوعات :A. R. Vahidi 1 , Gh. Asadi Kordshooli 2 , Z. Azimzadeh 3
1 - Department of Mathematics, Shahr-e-Rey Branch, Islamic Azad University
2 - Department of Physics, Shahr-e-Rey Branch, Islamic Azad University
3 - Department of Mathematics, Science and Research Branch, Islamic Azad University
الکلمات المفتاحية: Adomian decomposition method, Differential equation, damped forced oscillator,
ملخص المقالة :
In this paper, we present a comparative study between the Adomian decomposition method and two classical well-known Runge-Kutta and central difference methods for the solution of damped forced oscillator problem. We show that the Adomian decomposition method for this problem gives more accurate approximations relative to other numerical methods and is easier to apply.
[1] Adomian G., Nonlinear Stochastic Systems Theory and Applications to Physics, Kluwer, Dordrecht, 1989.
[2] Adomian G., Solving Frontier Problems of Physics: The Decomposition Method, Kluwer, Dordrecht, 1994.
[3] Yee E., Application of the decomposition method to the solution of the reaction- convection-diffusion equation, App. Math. And Computation, 56, 1-27, 1993.
[4] El-Sayed S. M., The modified decomposition method for solving non linear algebraic equations, App. Math. And Computation, 132, 589-597, 2002.
[5] Babolian E. and Biazar J., Solving the Problem of Biological Species Living Together by Adomian Decomposition Method, App. Math. And Computation 129, 339 -343, 2002.
[6] Babolian E. and Biazar J., Solving Concrete Examples by Adomian Method, App. Math. And Computation, 135, 161-167, 2003.
[7] Babolian E., Vahidi A. R. and Asadi Cordshooli G., Solving differential equations by decomposition Method, App. Math. And Computation, 167, 1150-1155, 2005.
[8] Wazwaz A. M., The modified decomposition method and Pade approximations for solving Thomas Fermi equations, App. Math. And Computation, 105, 11-19, 1999.
[9] Wazwaz A. M., A comparison between Adomian decomposition method and Taylor series method in the series solution, App. Math. And Computation, 97, 37-44, 1998.
[10] Rach R., On the Adomian decomposition method and comparison with Picard's method, J. Math. Anal. Appl., 128 , 480-483,1987.
[11] Edwards J. T., Roberts J. A., Ford, N. J., A comparison of Adomian's decomposition method and Runge Kutta methods for approximate solution of some predator prey model equation, Numerical Analysis Report, No. 309, 1997.
[12] El-Sayed S. M., Abdol-Aziz M. R., A comparison of Adomian's decomposition method and wavelet-Galerkin method for solving integro-differential equations, App. Math. And Computation, 136, 151-159, 2003.
[13] Bellomo N., and Sarafyan D., On a Comparison between Adomian's Decomposision Method and Picard Iteration, J. Math. Anal. Applic., No. 123, 1987.
[14] Babolian E., Biazar J., and Vahidi A., On the decomposition method for system of linear equations and system of linear Volterra integral equations, App. Math. Comput., 147, 19-27, 2004.
[15] Goldstein H., Cassical mechanics, Addison-Wesley, Massachusetts, 1980.
[16] Thomsen J. J., Vibrations and stability order and chaos, Mcgraw-Hill, London, 1997.
[17] Bhat Rama B., and Dukkipati V., Advanced dynamics, Alpha Science, Pangbourne, 2001.
[18] Simmons G. F., Differential equations with applications and historical notes, Mcgraw- Hill, London, 1972.
[19] Cherruault Y., Convergence of Adomian's method, Kybernets, 18(2), 31-39, 1989.
[20] Cherruault Y., Some new results for convergence of Adomian's method applied to integral equations, Matl. Comput. Modeling, 16(2), 85-93, 1992.
[21] Adomian G., A review of the Decomposition method in applied mathematics, J. Math. Anal. Appl. 135, 501-544, 1988.
[22] Burden R. L., Dauglas Faires J., Numreical Analysis, Seventh Edition, Brooks/Cole, 2001.
