Analytic and numerical solution for duffing equations

  • Authors

    • Majeed AL-Jawary Head of Department of Mathematics, College of Education Ibn-AL-Haitham, Baghdad University, Baghdad, Iraq
    • Sayl Abd- AL- Razaq Department of Mathematics, College of Education Ibn-Al-Haithem, Baghdad University, Baghdad
    2016-03-18
    https://doi.org/10.14419/ijbas.v5i2.5838
  • Daftardar Gejji and Hossein Jafari have proposed a new iterative method for solving many of the linear and nonlinear equations namely (DJM). This method proved already the effectiveness in solved many of the ordinary differential equations, partial differ

  • Abstract

    Daftardar Gejji and Hossein Jafari have proposed a new iterative method for solving many of the linear and nonlinear equations namely (DJM). This method proved already the effectiveness in solved many of the ordinary differential equations, partial differential equations and integral equations. The main aim from this paper is to propose the Daftardar-Jafari method (DJM) to solve the Duffing equations and to find the exact solution and numerical solutions. The proposed (DJM) is very effective and reliable, and the solution is obtained in the series form with easily computed components. The software used for the calculations in this study was MATHEMATICA® 9.0.

  • References

    1. [1] L-J. Sheu, H-K. Chen, J-H. Chen, L-M. Tam , Chaotic Dynamics of the Fractionally Damped Duffing Equation, Chaos Solitons and Fractals, 32 (2007) 1459-1468. http://dx.doi.org/10.1016/j.chaos.2005.11.066.

      [2] E. Y. (Agadjanov), Numerical solution of Duffing equation by the Laplace decomposition algorithm, Applied Mathematics and Computation 177 (2006) 572–580. http://dx.doi.org/10.1016/j.amc.2005.07.072.

      [3] Z. Feng, G. Chen, S-B Hsu, A qualitative Study of Damped Equation and Applications, Discrete and Continuous Dynamical Systems - Series B, Edinburg, 6(2005) 1097 - 1112.

      [4] S. Nourazar, A. Mirzabeigy, Approximate Solution for Nonlinear Duffing Oscillator with Damping Effect Using The modified Differential Transform Method, Scientia Iranica, Transactions B: Mechanical Engineering 20 (2013) 364–368.

      [5] S. Balaji, A New Approach For Solving Duffing Equations Involving Both Integral And Non- Integral Forcing Terms, Ain Shams Engineering Journal, 5 (2014), 985–990. http://dx.doi.org/10.1016/j.asej.2014.04.001.

      [6] M. Turkyilmazoglu, an Effective Approach for Approximate Analytical Solutions of the Damped Duffing Equation, Physica Scripta, 86 (2012), 1–6. http://dx.doi.org/10.1088/0031-8949/86/01/015301.

      [7] Y. Khan, H. Vazquez – Leal, N. Faraz, An Effective New Iterative Method For Oscillator Differential Equation, Scientia Iranica A, 19(2012), 1473-1477. http://dx.doi.org/10.1016/j.scient.2012.10.018.

      [8] Bender, C. M, Orszag, S. A, Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and Perturbation Theory, Springer, 1999, pp. 545–551. http://dx.doi.org/10.1007/978-1-4757-3069-2.

      [9] M. Khalid, M. Sultana, U. Arshad, M. Shoaib, A Comparison between New Iterative Solutions of Non- Linear Oscillator Equation, International Journal of Computer Applications, 128(2015), 1-5. http://dx.doi.org/10.5120/ijca2015906501.

      [10] B. Bulbul, M. Sezer, Numerical Solution of Duffing Equation by Using an Improved Taylor Matrix Method, Journal of Applied Mathematics, Volume 2013, Article ID 691614, 6 pages.

      [11] M. Najafi, M. Moghimi, H. Massah, H. Khoramishad, M. Daemi, On the Application of Adomian Decomposition Method and Oscillation Equations, The 9th International Conference on Applied Mathematics, Istanbul, Turkey, 2006.

      [12] V. Daftardar-Gejji, H. Jafari, An iterative method for solving nonlinear functional equations, Journal of Mathematical Analysis and Applications, 316(2006) 753–763. http://dx.doi.org/10.1016/j.jmaa.2005.05.009.

      [13] S. Bhalekar, V. Daftardar-Gejji, Convergence of the New Iterative Method, International Journal of Differential Equations, 2011, Article ID 989065, 10 pages.

      [14] A.M. Wazwaz,, Linear and Nonlinear Intagral Equations Methods and Applications, Saint Xavier University, Higher Education Press, Beijing and Springer-Varleg Berlin Heidlberg, 2011.

      [15] J.Duan, R. Rach, A.M. Wazwaz, Steady-state concentrations of carbon dioxide absorbed into phenyl glycidyl ether solutions by the Adomian decomposition method. Journal of Mathematical Chemistry, 53 (2015) 1054–1067. http://dx.doi.org/10.1007/s10910-014-0469-z.

      [16] M.A. AL-Jawary, G. H. Radhi, The variational Iteration Method for calculating carbon dioxide absorbed into phenyl glycidyl ether. IOSR Journal of Mathematics, 11 (2015) 99–105.

      [17] George. Adomain, solving frontier problems of physics: the decomposition method, Springer- science+ Business madia, B. V. (1994)238-239.

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  • How to Cite

    AL-Jawary, M., & Abd- AL- Razaq, S. (2016). Analytic and numerical solution for duffing equations. International Journal of Basic and Applied Sciences, 5(2), 115-119. https://doi.org/10.14419/ijbas.v5i2.5838

    Received date: 2016-02-06

    Accepted date: 2016-03-13

    Published date: 2016-03-18