# Additive self-similar approximants

## TL;DR

This paper introduces additive self-similar approximants, a new method based on self-similar approximation theory, demonstrating superior accuracy and convergence compared to Pade approximants in applied mathematics problems.

## Contribution

The paper presents a novel additive self-similar approximation method that improves accuracy and convergence over existing approximation techniques.

## Key findings

- Demonstrates good numerical convergence with exact solutions
- Shows the method is more accurate than Pade approximants
- Provides comparison with other approximation methods

## Abstract

A novel type of approximants is introduced, being based on the ideas of self-similar approximation theory. The method is illustrated by the examples possessing the structure typical of many problems in applied mathematics. Good numerical convergence is demonstrated for the cases that can be compared with exact solutions, when these are available. The method is shown to be not less and as a rule essentially more accurate than that of Pade approximants. Comparison with other approximation methods is also given.