Fourth-order two-step iterative methods for determining multiple zeros of non-linear equations

Abstract

In this paper, we describe and analyse two two-step iterative methods for finding multiple zeros of non-linear equations. We prove that the methods have fourth-order convergence. The methods calculate the multiple zeros with high accuracy. These are the first two-step multiple zero finding methods. The numerical tests show their better performance in the case of algebraic as well as non-algebraic equations

Keywords:

• Convergence order
• Multiple zeros
• Non-linear equations
• Predictor–corrector methods
• Two-step iterative methods