On a Parameter-controlled Method for Multiple Zeros

Abstract

For a parameter-controlled Newton-secant method, we investigate the complex dynamics with the stability surfaces and parameter spaces using Möbious conjugacy map applied to the form $((z-A) (z-B))^m$. The basins of attraction of test functions is illustrated according to the color palette. The nonlinear equation related to blood rheology model has been employed to show the basins of attraction.