Basin attractors for derivative-free methods to find simple roots of nonlinear equations

Abstract

Many methods exist for solving nonlinear equations. Several of these methods are derivative-free. One of the oldest is the secant method where the derivative is replaced by a divided difference. Clearly such method will need an additional starting value. Here we consider several derivative-free methods and compare them using the idea of basin of attraction.

Keywords

• Basin of attraction
• derivative-free methods
• simple roots
• nonlinear equations