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

Yi He, Xing Biao Hu, Hon Wah TAM, Ying Nan Zhang

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

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 ∈-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 ∈-algorithm, we have therefore arrived at a generalization of this algorithm. Finally, numerical experiments on the new algorithm are presented.

Original languageEnglish
Pages (from-to)194-212
Number of pages19
JournalEuropean Journal of Applied Mathematics
Volume27
Issue number2
DOIs
Publication statusPublished - 1 Apr 2016

Scopus Subject Areas

  • Applied Mathematics

User-Defined Keywords

  • G-transformation
  • Lattice Boussinesq equation
  • Lotka-Volterra equation
  • Multistep ∈-algorithm

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