Volume 4, Issue 4
The Multi-Step Differential Transform Method and Its Application to Determine the Solutions of Non-Linear Oscillators

Vedat Suat Ertürk, Zaid M. Odibat & Shaher Momani

Adv. Appl. Math. Mech., 4 (2012), pp. 422-438.

Published online: 2012-04

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  • Abstract

In this paper, a reliable algorithm based on an adaptation of the standard differential transform method is presented, which is the multi-step differential transform method (MSDTM). The solutions of non-linear oscillators were obtained by MSDTM. Figurative comparisons between the MSDTM and the classical fourth-order Runge-Kutta method (RK4) reveal that the proposed technique is a promising tool to solve non-linear oscillators.

  • Keywords

Non-linear oscillatory systems, differential transform method, numerical solution.

  • AMS Subject Headings

74H15, 35E15, 37M05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-4-422, author = {}, title = {The Multi-Step Differential Transform Method and Its Application to Determine the Solutions of Non-Linear Oscillators}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2012}, volume = {4}, number = {4}, pages = {422--438}, abstract = {

In this paper, a reliable algorithm based on an adaptation of the standard differential transform method is presented, which is the multi-step differential transform method (MSDTM). The solutions of non-linear oscillators were obtained by MSDTM. Figurative comparisons between the MSDTM and the classical fourth-order Runge-Kutta method (RK4) reveal that the proposed technique is a promising tool to solve non-linear oscillators.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.10-m1138}, url = {http://global-sci.org/intro/article_detail/aamm/128.html} }
TY - JOUR T1 - The Multi-Step Differential Transform Method and Its Application to Determine the Solutions of Non-Linear Oscillators JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 422 EP - 438 PY - 2012 DA - 2012/04 SN - 4 DO - http://doi.org/10.4208/aamm.10-m1138 UR - https://global-sci.org/intro/article_detail/aamm/128.html KW - Non-linear oscillatory systems, differential transform method, numerical solution. AB -

In this paper, a reliable algorithm based on an adaptation of the standard differential transform method is presented, which is the multi-step differential transform method (MSDTM). The solutions of non-linear oscillators were obtained by MSDTM. Figurative comparisons between the MSDTM and the classical fourth-order Runge-Kutta method (RK4) reveal that the proposed technique is a promising tool to solve non-linear oscillators.

Vedat Suat Ertürk, Zaid M. Odibat & Shaher Momani. (1970). The Multi-Step Differential Transform Method and Its Application to Determine the Solutions of Non-Linear Oscillators. Advances in Applied Mathematics and Mechanics. 4 (4). 422-438. doi:10.4208/aamm.10-m1138
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