On Family of Simultaneous Method for Finding Distinct as Well as Multiple Roots of Non-linear Equation

Abstract

We construct a family of 2-step simultaneous methods for determining all the distinct roots of single variable non-linear equations. We further extend this family of simultaneous methods to the case of multiple roots. It is proved that both the family of methods are of convergence order eight and has better computation efficiency as compared to some other simultaneous methods in the literature. At the end, numerical test examples are given to demonstrate the efficiency and performance of the newly constructed simultaneous methods.