On The Periodic Solution of the Helmholtz Equations Using the Modified Differential Transform Method

Nageswara Rao Boggarapu, J. Peter Praveen


The modified differential transform method (MDTM) is formed the subject by a large number of publications. The MDTM is claimed to be an efficient method for obtaining periodic solution for the non-linear oscillatory systems. This paper examines the periodic solution of Helmholtz equation of motion having a non-odd restoring force function. The behavior of oscillations is expected to be different for the same magnitude of positive and negative amplitudes. The solution of the Helmholtz equation obtained utilizing the MDTM is unable to capture the unequal magnitudes of the positive and negative amplitudes for the specified frequency or the period. In addition to the presentation on the drawbacks in the MDTM, this paper recommends the harmonic balance method for obtaining accurate periodic solution of nonlinear Duffing oscillators.

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