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# Application of the Differential Transform Method for Solving Periodic Solutions of Strongly Non-linear Oscillators

Hsin-Ping Chu1, Cheng-Ying Lo2

Kao Yuan University, Department of Mechanical and Automation Engineering, Kaohsiung, Taiwan
National Formosa University, Department of Aeronautical Engineering, Yulin, Taiwan (Corresponding author)

Computer Modeling in Engineering & Sciences 2011, 77(3&4), 161-172. https://doi.org/10.3970/cmes.2011.077.161

## Abstract

This paper presents the application of the differential transform method to solve strongly nonlinear equations with cubic nonlinearities and self-excitation terms. First, the equations are transformed by the differential transform method into the algebra equations in terms of the transformed functions. Secondly, the higher-order transformed functions are calculated in terms of other lower-order transformed functions through the iterative procedure. Finally, the solutions are approximated by the n-th partial sum of the infinite series obtained by the inverse differential transform. Two strongly nonlinear equations with different coefficients and initial conditions are given as illustrative examples.

## Keywords

APA Style
Chu, H., Lo, C. (2011). Application of the differential transform method for solving periodic solutions of strongly non-linear oscillators. Computer Modeling in Engineering & Sciences, 77(3&4), 161-172. https://doi.org/10.3970/cmes.2011.077.161
Vancouver Style
Chu H, Lo C. Application of the differential transform method for solving periodic solutions of strongly non-linear oscillators. Comput Model Eng Sci. 2011;77(3&4):161-172 https://doi.org/10.3970/cmes.2011.077.161
IEEE Style
H. Chu and C. Lo, "Application of the Differential Transform Method for Solving Periodic Solutions of Strongly Non-linear Oscillators," Comput. Model. Eng. Sci., vol. 77, no. 3&4, pp. 161-172. 2011. https://doi.org/10.3970/cmes.2011.077.161

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