The Multi-Step Differential Transform Method and Its Application to Determine the Solutions of Non-Linear Oscillators
Year: 2012
Author: Vedat Suat Ertürk, Zaid M. Odibat, Shaher Momani
Advances in Applied Mathematics and Mechanics, Vol. 4 (2012), Iss. 4 : pp. 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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.10-m1138
Advances in Applied Mathematics and Mechanics, Vol. 4 (2012), Iss. 4 : pp. 422–438
Published online: 2012-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Non-linear oscillatory systems differential transform method numerical solution.
Author Details
-
Dynamic Analysis of Lower Limb Exoskeleton Motion and Control Using Differential Transform Method
Adeleye, Olurotimi A. | Ekine, Tamunomiete S. | Yinusa, Ahmed A.Journal of Biomimetics, Biomaterials and Biomedical Engineering, Vol. 51 (2021), Iss. P.77
https://doi.org/10.4028/www.scientific.net/JBBBE.51.77 [Citations: 0] -
Torsional Alfvén waves and the period ratio P 1/P 2 in spicules
Ebadi, H. | Shahmorad, S.Astrophysics and Space Science, Vol. 353 (2014), Iss. 1 P.25
https://doi.org/10.1007/s10509-014-2003-y [Citations: 2] -
Power System Time Domain Simulation Using a Differential Transformation Method
Liu, Yang | Sun, Kai | Yao, Rui | Wang, BinIEEE Transactions on Power Systems, Vol. 34 (2019), Iss. 5 P.3739
https://doi.org/10.1109/TPWRS.2019.2901654 [Citations: 41] -
The kinematics behaviour of coupled pendulum using differential transformation method
Erturk, V.S. | Asad, J. | Jarrar, R. | Shanak, H. | Khalilia, H.Results in Physics, Vol. 26 (2021), Iss. P.104325
https://doi.org/10.1016/j.rinp.2021.104325 [Citations: 2] -
Magnetohydrodynamics natural convection of nanofluid flow over a vertical circular cone embedded in a porous medium and subjected to thermal radiation
Sobamowo, MG | Yinusa, AA | Aladenusi, ST | Salami, MOInternational Journal of Petrochemical Science & Engineering, Vol. 5 (2020), Iss. 1 P.22
https://doi.org/10.15406/ipcse.2020.05.00119 [Citations: 0] -
Nonlinear analysis of memcapacitor-based hyperchaotic oscillator by using adaptive multi-step differential transform method
Taheri, Alireza Ghomi | Setoudeh, Farbod | Tavakoli, Mohammad Bagher | Feizi, EsmaeilChaos, Solitons & Fractals, Vol. 159 (2022), Iss. P.112122
https://doi.org/10.1016/j.chaos.2022.112122 [Citations: 3] -
The period ratio P 1 / P 2 $P_{1}/P_{2}$ of torsional Alfvén waves with steady flows in spicules
Ebadi, H. | Shahmorad, S. | Vasheghani Farahani, S.Astrophysics and Space Science, Vol. 361 (2016), Iss. 4
https://doi.org/10.1007/s10509-016-2716-1 [Citations: 1] -
A novel time integration formulation for nonlinear dynamic analysis
Rezaiee-Pajand, M. | Hashemian, M. | Bohluly, A.Aerospace Science and Technology, Vol. 69 (2017), Iss. P.625
https://doi.org/10.1016/j.ast.2017.07.032 [Citations: 25] -
Numerical Analysis of an Airfoil with Nonlinear Stiffness Using DTM
Shali, S. | Jafarali, Parol | Nagaraja, S. R.Iranian Journal of Science and Technology, Transactions of Mechanical Engineering, Vol. 47 (2023), Iss. 4 P.2059
https://doi.org/10.1007/s40997-023-00611-7 [Citations: 0] -
High accuracy analysis for motion of a spherical particle in plane Couette fluid flow by Multi-step Differential Transformation Method
Hatami, M. | Sheikholeslami, M. | Domairry, G.Powder Technology, Vol. 260 (2014), Iss. P.59
https://doi.org/10.1016/j.powtec.2014.02.057 [Citations: 62] -
Approximate analytical solutions to nonlinear peristaltic flow with temperature-dependent viscosity parameters: Application of multi-step differential transform method (MsDTM)
Elogail, M.A. | Elshekhipy, A.A.Canadian Journal of Physics, Vol. 96 (2018), Iss. 3 P.287
https://doi.org/10.1139/cjp-2017-0070 [Citations: 9] -
Damping efficiency of the Duffing system with additional fractional terms
Rysak, A. | Sedlmayr, M.Applied Mathematical Modelling, Vol. 111 (2022), Iss. P.521
https://doi.org/10.1016/j.apm.2022.06.037 [Citations: 9] -
Modified differential transformation method for solving nonlinear dynamic problems
Rezaiee-Pajand, M. | Hashemian, M.Applied Mathematical Modelling, Vol. 47 (2017), Iss. P.76
https://doi.org/10.1016/j.apm.2017.03.003 [Citations: 9] -
A Dynamized Power Flow Method Based on Differential Transformation
Liu, Yang | Sun, Kai | Dong, JiaojiaoIEEE Access, Vol. 8 (2020), Iss. P.182441
https://doi.org/10.1109/ACCESS.2020.3028060 [Citations: 14] -
Nonlinear Steady State and Dynamic Response Analysis of Focused Ultrasound Actuated Smart Biomaterials
Adeleye, Olurotimi | Yinusa, Ahmed | Konigbagbe, StephenApplied Mechanics and Materials, Vol. 906 (2022), Iss. P.1
https://doi.org/10.4028/p-6fg7f8 [Citations: 1] -
Torsional waves with force-free magnetic fields in solar plasma structures
Ebadi, H | Shahmorad, S | Vasheghani Farahani, SMonthly Notices of the Royal Astronomical Society, Vol. 502 (2021), Iss. 4 P.4930
https://doi.org/10.1093/mnras/stab334 [Citations: 1] -
Iterative Multistep Reproducing Kernel Hilbert Space Method for Solving Strongly Nonlinear Oscillators
Maayah, Banan | Bushnaq, Samia | Momani, Shaher | Abu Arqub, OmarAdvances in Mathematical Physics, Vol. 2014 (2014), Iss. P.1
https://doi.org/10.1155/2014/758195 [Citations: 11] -
A new modified polynomial-based optimal control design approach
Monfared, Morteza Nazari | Fakharian, Ahmad | Menhaj, Mohammad BagherProceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, Vol. 235 (2021), Iss. 3 P.355
https://doi.org/10.1177/0959651820946891 [Citations: 3] -
Numerical Multistep Approach for Solving Fractional Partial Differential Equations
Al-Smadi, Mohammed | Freihat, Asad | Khalil, Hammad | Momani, Shaher | Ali Khan, RahmatInternational Journal of Computational Methods, Vol. 14 (2017), Iss. 03 P.1750029
https://doi.org/10.1142/S0219876217500293 [Citations: 87]