A multi-step differential transform method and application to non-chaotic or chaotic systems
TL;DR: A reliable new algorithm of DTM is proposed, namely multi-step DTM, which will increase the interval of convergence for the series solution, and is applied to Lotka-Volterra, Chen and Lorenz systems.
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Abstract: The differential transform method (DTM) is an analytical and numerical method for solving a wide variety of differential equations and usually gets the solution in a series form. In this paper, we propose a reliable new algorithm of DTM, namely multi-step DTM, which will increase the interval of convergence for the series solution. The multi-step DTM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions for systems of differential equations. This new algorithm is applied to Lotka-Volterra, Chen and Lorenz systems. Then, a comparative study between the new algorithm, multi-step DTM, classical DTM and the classical Runge-Kutta method is presented. The results demonstrate reliability and efficiency of the algorithm developed.
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Citations
Study of a third grade non-Newtonian fluid flow between two parallel plates using the multi-step differential transform method
TL;DR: It has been attempted to show the reliability and performance of the MDTM in comparison with the numerical method (fourth-order Runge-Kutta) and other analytical methods such as HPM, HAM and DTM in solving this problem.
159
Numerical Multistep Approach for Solving Fractional Partial Differential Equations
TL;DR: In this paper, a multistep reduced differential transformation method (MRDTM) is proposed for one-dimensional fractional heat equations with time fractional derivatives subjected to the appropriate initial condition.
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A numeric-analytic method for approximating a giving up smoking model containing fractional derivatives
TL;DR: The multistep generalized differential transform method (for short MSGDTM) is employed to compute accurate approximate solutions to a giving up smoking model of fractional order, and the unique positive solution for the fractions of the model is presented.
98
On the solutions of time-fractional reaction–diffusion equations
TL;DR: In this article, a new application of generalized differential transform method (GDTM) has been used for solving time-fractional reaction-diffusion equations, and some examples are provided.
80
High accuracy analysis for motion of a spherical particle in plane Couette fluid flow by Multi-step Differential Transformation Method
TL;DR: In this paper, the authors solved the coupled equations of particle motion in Couette fluid flow by Multi-step Differential Transformation Method (Ms-DTM) considering the rotation and shear effects on lift force and neglecting gravity.
72
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Yet another chaotic attractor
Guanrong Chen,Tetsushi Ueta +1 more
TL;DR: In this paper, the authors reported the finding of a chaotic at tractor in a simple three-dimensional autonomous system, which resembles some familiar features from both the Lorenz and Rossler at tractors.
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TL;DR: Three-dimensional differential transform method has been introduced and fundamental theorems have been defined for the first time and exact solutions of linear and non-linear systems of partial differential equations have been investigated.
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Bifurcation analysis of chen's equation
Tetsushi Ueta,Guanrong Chen +1 more
TL;DR: Some basic dynamical properties and various bifurcations of Chen's equation are investigated, thereby revealing its different features from some other chaotic models such as its origin, the Lorenz system.
A generalized differential transform method for linear partial differential equations of fractional order
Zaid Odibat,Shaher Momani +1 more
TL;DR: A new generalization of the two-dimensional differential transform method is developed that will extend the application of the method to linear partial differential equations with space- and time-fractional derivatives, generalized Taylor’s formula and Caputo fractional derivative.
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