Journal of Numerical Mathematics, Volume (22), No (4), Year (2014-2) , Pages (343-362)

Title : ( On the piecewise-spectral homotopy analysis method and its convergence: solution of hyperchaotic L¨u system )

Authors: S. S.MOTSA , Hassan Saberi Nik , Sohrab Effati , Jafar Saberi Najafi ,

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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.

Keywords

, hyperchaotic system, Banach’s fixed point theorem, piecewise-spectral homotopy analysis method, spectral
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@article{paperid:1046751,
author = {S. S.MOTSA and Saberi Nik, Hassan and Effati, Sohrab and Saberi Najafi, Jafar},
title = {On the piecewise-spectral homotopy analysis method and its convergence: solution of hyperchaotic L¨u system},
journal = {Journal of Numerical Mathematics},
year = {2014},
volume = {22},
number = {4},
month = {February},
issn = {1570-2820},
pages = {343--362},
numpages = {19},
keywords = {hyperchaotic system; Banach’s fixed point theorem; piecewise-spectral homotopy analysis method; spectral collocation},
}

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%0 Journal Article
%T On the piecewise-spectral homotopy analysis method and its convergence: solution of hyperchaotic L¨u system
%A S. S.MOTSA
%A Saberi Nik, Hassan
%A Effati, Sohrab
%A Saberi Najafi, Jafar
%J Journal of Numerical Mathematics
%@ 1570-2820
%D 2014

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