Third-order and fourth-order iterative methods for finding multiple and distinct zeros of non-linear equations

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