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Licensed Unlicensed Requires Authentication Published by De Gruyter November 25, 2014

On the piecewise-spectral homotopy analysis method and its convergence: solution of hyperchaotic Lü system

  • S. S. Motsa , H. Saberi Nik EMAIL logo , S. Effati and J. Saberi-Nadjafi

Abstract

- In this paper, a novel modification of the spectral-homotopy analysis method (SHAM) technique for solving highly nonlinear initial value problems that model systems with chaotic and hyper-chaotic behaviour is presented. The proposed method is based on implementing the SHAM on a sequence of multiple intervals thereby increasing it’s radius of convergence to yield highly accuratemethod which is referred to as the piece-wise spectral homotopy analysis method (PSHAM). We investigate the application of the PSHAM to the L¨u system [20] which is well known to display periodic, chaotic and hyper-chaotic behaviour under carefully selected values of it’s governing parameters. Existence and uniqueness of solution of SHAM that give a guarantee of convergence of SHAM, has been discussed in details. Comparisons are made between PSHAMgenerated results and results from literature and Runge-Kutta generated results and good agreement is observed.

Received: 2012-10-19
Revised: 2013-8-13
Published Online: 2014-11-25
Published in Print: 2014-12-1

© 2014 by Walter de Gruyter Berlin/Boston

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