Discrete soliton equations and convergence acceleration algorithms

Atsushi Nagai; Junkichi Satsuma

doi:10.1016/0375-9601(95)00865-9

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arXiv · solv-int/9511001

Discrete soliton equations and convergence acceleration algorithms

Atsushi Nagai·Junkichi Satsuma

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Abstract

Some of the well-known convergence acceleration algorithms, when viewed as two-variable difference equations, are equivalent to discrete soliton equations. It is shown that the $η-$algorithm is nothing but the discrete KdV equation. In addition, one generalized version of the $ρ-$algorithm is considered to be integrable discretization of the cylindrical KdV equation.

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Atsushi Nagai, Junkichi Satsuma. 1995-11-07. Discrete soliton equations and convergence acceleration algorithms. https://doi.org/10.1016/0375-9601(95)00865-9

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