Convergence acceleration for the BLUES function method

TL;DR

This paper compares four iterative procedures within the BLUES function method and variational iteration method, applying them to a nonlinear differential equation to analyze convergence and accuracy improvements.

Contribution

It provides a detailed comparison of iterative procedures in the BLUES function method, highlighting convergence acceleration techniques for nonlinear differential equations.

Findings

Modified methods improve convergence speed

Differences in approximants highlight method effectiveness

Error analysis shows accuracy improvements

Abstract

A detailed comparison is made between four different iterative procedures: Picard, Ishikawa, Mann and Picard-Krasnoselskii, within the framework of the BLUES function method and the variational iteration method. The resulting modified methods are subsequently applied to a nonlinear reaction-diffusion-advection differential equation to generate approximations to the known exact solution. The differences between the BLUES function method and the variational iteration method are illustrated by studying the approximants and the error between the obtained approximants and the exact solution.