Basins of attraction for Zhou-Chen-Song fourth order family of methods for multiple roots

Abstract

There are very few optimal fourth order methods for solving nonlinear algebraic equations having roots of multiplicity m. In a previous paper we have compared 5 such methods, two of which require the evaluation of the (m - 1)th root. We have used the basin of attraction idea to recommend the best optimal fourth order method. Here we suggest to improve on the best of those five, namely Zhou-Chen-Song method by showing how to choose the best weight function.