Fourth Order Methods for Finding Multiple as well as Distinct Zeros of Non-linear Equations ∗ Nazir Ahmad Mir † Department of Mathematics, COMSATS Institute of Information Technology, Plot No. 30, Sector H-8/1, Islamabad 44000, Pakistan and Farooq Ahmad ‡ , Muhammad Raza § , Tahira Nawaz ¶ Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, Pakistan Received February 17, 2009, Accepted May 19, 2009. Tamsui Oxford Journal of Mathematical Sciences 26(3) (2010) 321-333 Aletheia University Abstract In this paper, we point out and analyse six two-step iterative meth- ods for finding multiple as well as distinct zeros of non-linear equations. We prove that the methods for multiple zeros as well as for distinct ze- ros 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. Keywords and Phrases: Two-step iterative methods, Predictor-corrector methods, Convergence-Order, Multiple zeros, Distinct zeros, Non-linear equa- tions. * 2000 Mathematics Subject Classification. Primary 34A34, 65H05. † Corresponding author. E-mail: nazirahmad.mir@gmail.com ‡ E-mail: farooqgujar@gmail.com § E-mail: mreza06r@gmail.com ¶ E-mail: tahira.nawaz@gmail.com