Application of the differential transformation method for the solution of the hyperchaotic Rössler system

2009 ◽  
Vol 14 (4) ◽  
pp. 1509-1514 ◽  
Author(s):  
M. Mossa Al-Sawalha ◽  
M.S.M. Noorani
Keyword(s):  
Transformation Method ◽  
Differential Transformation Method ◽  
Differential Transformation ◽  
Rossler System ◽  
Rössler System

scholarly journals Implementation of multi-step differentialtransformation method for hyperchaotic Rossler system

2016 ◽  
Vol 6 (1) ◽  
pp. 4
Author(s):  
Jafar Biazar ◽  
Tahereh Houlari ◽  
Roxana Asayesh
Keyword(s):  
Fourth Order ◽  
Transformation Method ◽  
Differential Transformation Method ◽  
Kutta Method ◽  
Powerful Technique ◽  
Differential Transformation ◽  
Runge Kutta Method ◽  
Rossler System ◽  
Rössler System ◽  
Runge Kutta

In this work, the multi-step differential transformation method (MSDTM) is applied to approximate a solution of the hyperchaotic Rossler system. MSDTM is adapted from the differential transformation method (DTM). In this method, DTM is implemented in each subinterval. Results are compared with a fourth-order Runge Kutta method and a standard DTM. The results show that the MSDTM is an efficient and powerful technique for solving hyperchaotic Rossler systems and this method is more accurate than DTM.

Differential transformation method for circular membrane vibrations

2020 ◽  
Vol 61(12) (2) ◽  
pp. 333-350
Author(s):  
Jaipong Kasemsuwan ◽  
◽  
Sorin Vasile Sabau ◽  
Uraiwan Somboon ◽  
◽  
...  
Keyword(s):  
Transformation Method ◽  
Differential Transformation Method ◽  
Circular Membrane ◽  
Differential Transformation ◽  
Membrane Vibrations

scholarly journals Differential Transformation Method (DTM) for Solving SIS and SI Epidemic Models

2017 ◽  
Vol 46 (10) ◽  
pp. 2007-2017
Author(s):  
M.Z. Ahmad ◽  
D. Alsarayreh ◽  
A. Alsarayreh ◽  
I. Qaralleh
Keyword(s):  
Transformation Method ◽  
Epidemic Models ◽  
Differential Transformation Method ◽  
Differential Transformation

scholarly journals Nonlinear Vibration Analysis of an Electrostatically Actuated Microbeam using Differential Transformation Method

2020 ◽  
Vol 2 (2) ◽  
Author(s):  
Gbeminiyi Musibau Sobamowo ◽  
A A. Yinusa ◽  
O. A. Adesina ◽  
O. M. Oyekeye
Keyword(s):  
Nonlinear Vibration ◽  
Nonlinear Problems ◽  
Transformation Method ◽  
Differential Transformation Method ◽  
Velocity Variation ◽  
Differential Transformation ◽  
Electrostatically Actuated ◽  
Homotopy Analysis ◽  
Comparison Of The Results ◽  
High Level

In this paper, nonlinear vibration of electrostatically actuated microbeam is analyzed using differential transformation method. The high level of accuracy of the analytical solutions of the method was established through comparison of the results of the solutions of exact analytical method, variational approach, homotopy analysis method and energy balance methods. Also, with the aid of the present analytical solution, the time response, velocity variation and the phase plots of the system are presented graphically. It is hope that the method will be widely applied to more nonlinear problems of systems in various fields of study. 

scholarly journals Analysis of beam-column elements on non-homogeneous soil using the differential transformation method

2021 ◽  
Author(s):  
Juan Sebastián Carvajal-Muñoz ◽  
Carlos Alberto Vega-Posada ◽  
Julio César Saldarriaga-Molina
Keyword(s):  
Boundary Conditions ◽  
Elastic Foundation ◽  
Mathematical Formulation ◽  
Transformation Method ◽  
Transverse Load ◽  
Differential Transformation Method ◽  
Differential Transformation ◽  
Pasternak Elastic Foundation ◽  
Wide Range ◽  
Homogeneous Soil

This paper describes an analytical approach to conduct an analysis of beam-column elements with generalized end-boundary conditions on a homogeneous or non-homogeneous Pasternak elastic foundation. The mathematical formulation utilized herein is that presented by the senior author in a recent work. The differential equation (DE) governing the behavior of the beam-column element is solved using the differential transformation method (DTM). The DTM offers practical advantages over other conventional approaches when solving the proposed structural model. The proposed formulation provides the flexibility to account for i) combined lateral and axial load at the ends of the element, ii) homogeneous or non-homogeneous soil, iii) Pasternak elastic foundation, and iv) an external arbitrary transverse load acting on the element. The effects of various slenderness ratios, pile-soil stiffness ratios, and classical and semirigid boundary conditions can be easily studied with the proposed formulation. Examples are presented to validate the accuracy of the model and its applicability over a wide range of analyses.

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