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Article Dans Une Revue Computers & Mathematics with Applications Année : 2010

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

Résumé

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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Dates et versions

hal-00430504 , version 1 (08-11-2009)

Identifiants

  • HAL Id : hal-00430504 , version 1

Citer

Zaid M. Odibat, Cyrille Bertelle, Moulay Aziz-Alaoui, Gérard H.E. Duchamp. A multi-step differential transform method and application to non-chaotic or chaotic systems. Computers & Mathematics with Applications, 2010, xx (xx), pp.xx-xx. ⟨hal-00430504⟩
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