# An efficient method to compute solitary wave solutions of fractional Korteweg-de Vries equations

## TL;DR

This paper introduces an efficient numerical method combining fixed-point iteration and extrapolation to accurately compute solitary wave solutions of fractional Korteweg-de Vries equations, enabling detailed analysis of wave properties.

## Contribution

The paper presents a novel, accelerated fixed-point iterative algorithm for computing solitary wave profiles of fractional KdV equations with improved convergence and accuracy.

## Key findings

- Enhanced convergence speed and accuracy in computing wave profiles.
- Validated numerical method through experiments and analysis.
- Enabled detailed investigation of wave properties like speed-amplitude relation.

## Abstract

Considered here is an efficient technique to compute approximate profiles of solitary wave solutions of fractional Korteweg-de Vries equations. The numerical method is based on a fixed-point iterative algorithm along with extrapolation techniques of acceleration. This combination improves the performance in both the velocity of convergence and the computation of profiles for limiting values of the fractional parameter. The algorithm is described and numerical experiments of validation are presented. The accuracy attained by the procedure can be used to investigate additional properties of the waves. This approach is illustrated here by analyzing the speed-amplitude relation.