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