A multi-step differential transform method and application to non-chaotic or chaotic systems

Computers & Mathematics with Applications

Odibat Z., Corson N., Aziz-Alaoui M.A., Bertelle C.

Labo. of Applied Maths., EA 3821, Le Havre University, France.


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

Keywords: Differential transform method, Multi-step differential transform method, Lotka–Volterra system, Chen system, Lorenz system

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