Paper Info
Title
On the piecewise-spectral homotopy analysis method and its convergence: solution of hyperchaotic Lü system.
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 Lu 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 PSHAM generated results and results from literature and Runge-Kutta generated results and good agreement is observed.
Year
DOI
Venue
2014
10.1515/jnma-2014-0015
JOURNAL OF NUMERICAL MATHEMATICS
Keywords
DocType
Volume
hyperchaotic system,Banach's fixed point theorem,piecewise-spectral homotopy analysis method,spectral collocation
Journal
22
Issue
ISSN
Citations 
4
1570-2820
0
PageRank 
References 
Authors
0.34
8
4
Name
Order
Citations
PageRank
Sandile Sydney Motsa16215.64
Hassan Saberi Nik2688.32
Effati Sohrab327630.31
Jafar Saberi-Nadjafi4849.28