Extrapolation and interpolation of asymptotic series by self-similar approximants

TL;DR

This paper introduces new self-similar approximant methods for extrapolating and interpolating asymptotic series, with applications to chemical physics and fluctuating fluid membranes, demonstrating improved accuracy and agreement with numerical data.

Contribution

It proposes novel variants of self-similar approximants to enhance the accuracy of asymptotic series extrapolation and interpolation, especially for complex physical systems.

Findings

Methods accurately predict the equation of state for strongly interacting systems.

Approach effectively describes properties of fluctuating fluid membranes.

Results align well with existing numerical data.

Abstract

The problem of extrapolation and interpolation of asymptotic series is considered. Several new variants of improving the accuracy of the self-similar approximants are suggested. The methods are illustrated by examples typical of chemical physics, when one is interested in finding the equation of state for a strongly interacting system. A special attention is payed to the study of the basic properties of fluctuating fluid membranes. It is shown that these properties can be well described by means of the method of self-similar approximants. For this purpose, the method has been generalized in order to give accurate predictions at infinity for a function, whose behavior is known only at the region of its variable close to zero. The obtained results for fluctuating fluid membranes are in good agreement with the known numerical data.