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Journal of Applied Mathematics
Volume 2013, Article ID 691614, 6 pages
Research Article

Numerical Solution of Duffing Equation by Using an Improved Taylor Matrix Method

1Department of Mathematics, Faculty of Science, Muğla University, 48000 Muğla, Turkey
2Department of Mathematics, Faculty of Science, Celal Bayar University, 45000 Manisa, Turkey

Received 30 December 2012; Revised 14 May 2013; Accepted 20 May 2013

Academic Editor: Han H. Choi

Copyright © 2013 Berna Bülbül and Mehmet Sezer. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We have suggested a numerical approach, which is based on an improved Taylor matrix method, for solving Duffing differential equations. The method is based on the approximation by the truncated Taylor series about center zero. Duffing equation and conditions are transformed into the matrix equations, which corresponds to a system of nonlinear algebraic equations with the unknown coefficients, via collocation points. Combining these matrix equations and then solving the system yield the unknown coefficients of the solution function. Numerical examples are included to demonstrate the validity and the applicability of the technique. The results show the efficiency and the accuracy of the present work. Also, the method can be easily applied to engineering and science problems.