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A new method to generate non-autonomous discrete integrable systems via convergence acceleration algorithms

Published online by Cambridge University Press:  07 September 2015

YI HE ,
XING-BIAO HU ,
HON-WAH TAM  and
YING-NAN ZHANG
YI HE
Affiliation:
Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, PR China email: [email protected]
XING-BIAO HU
Affiliation:
LSEC, Institute of Computational Mathematics and Scientific Engineering Computing, AMSS, Chinese Academy of Sciences, P.O.Box 2719, Beijing 100190, PR [email protected]
HON-WAH TAM
Affiliation:
Department of Computer Science, Hong Kong Baptist University, Kowloon Tong, Hong Kong, PR [email protected]
YING-NAN ZHANG
Affiliation:
School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, PR [email protected]
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Abstract

In this paper, we propose a new algebraic method to construct non-autonomous discrete integrable systems. The method starts from constructing generalizations of convergence acceleration algorithms related to discrete integrable systems. Then the non-autonomous version of the corresponding integrable systems are derived. The molecule solutions of the systems are also obtained. As an example of the application of the method, we propose a generalization of the multistep ϵ-algorithm, and then derive a non-autonomous discrete extended Lotka–Volterra equation. Since the convergence acceleration algorithm from the lattice Boussinesq equation is just a particular case of the multistep ϵ-algorithm, we have therefore arrived at a generalization of this algorithm. Finally, numerical experiments on the new algorithm are presented.

Keywords

multistep ϵ-algorithmG-transformationLotka–Volterra equationLattice Boussinesq equation
Type
Papers
Information
European Journal of Applied Mathematics , Volume 27 , Issue 2 , April 2016 , pp. 194 - 212
Copyright
Copyright © Cambridge University Press 2015 

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