Derivative free iterative simultaneous method for finding distinct roots of polynomial equation

Abstract

In this article, we present a new derivative free simultaneous method for determining in particular all the distinct roots of polynomial equation. A modification in Weierstrass correction is used to construct tenth order derivative free simultaneous method, using only four function evaluation per cycle. Convergence analysis proved that the order of convergence of derivative free simultaneous method is ten and has a better computational efficiency as compared to other simultaneous methods in the literature. Numerical test examples are provided to demonstrate the performance and efficiency of the newly constructed derivative free simultaneous method.

Keywords

• Distinct roots
• Non-linear equation
• Iterative methods
• Simultaneous method
• Derivative free method
• Computational efficiency