Basins of attraction for family of Popovski’s methods and their extension to multiple roots

Abstract

In this paper we revisit Popovski’s family of methods for simple roots. We compare several members using basins of attraction visually and qualitatively by comparing the run-time on several examples, the average number of iterations and the number of divergent points. We chose 5 different members of the family. We also develop an equivalent family of methods for multiple roots and compare several members on six different numerical examples.

Keywords

• Nonlinear equations
• simple roots
• multiple roots
• basins of attraction
• Popovski's method