From Asymptotic Series to Self-Similar Approximants

TL;DR

This paper reviews a unified approach that transforms asymptotic series into accurate self-similar approximants, demonstrating its effectiveness in solving complex physics problems with simplicity and precision.

Contribution

It introduces a cohesive framework connecting asymptotic series, optimized perturbation, and self-similar approximation theories, highlighting their interrelations and practical applications.

Findings

The approach effectively constructs accurate solutions from asymptotic series.

Applications show the method combines simplicity with high accuracy.

The interrelation of the theories enhances the solution process.

Abstract

The review presents the development of an approach of constructing approximate solutions to complicated physics problems, starting from asymptotic series, through optimized perturbation theory, to self-similar approximation theory. The close interrelation of underlying ideas of these theories is emphasized. Applications of the developed approach are illustrated by typical examples demonstrating that it combines simplicity with good accuracy.