Study of a Biparametric Family of Iterative Methods

الملخص EN

The dynamics of a biparametric family for solving nonlinear equations is studied on quadratic polynomials.

This biparametric family includes the c -iterative methods and the well-known Chebyshev-Halley family.

We find the analytical expressions for the fixed and critical points by solving 6-degree polynomials.

We use the free critical points to get the parameter planes and, by observing them, we specify some values of ( α ,   c ) with clear stable and unstable behaviors.