Asian Journal of Scientific Research 1992-1454 2077-2076 Asian Network for Scientific Information 10.3923/ajsr.2018.409.414 Wartono Soleh M. Suryani I. Zulakmal Muhafzan 3 2018 11 3 Background and Objective: The Chebyshev-Halley is an third order iterative method that be used to find the roots of a nonlinear equation. This study is presented a new variant of Chebyshev-Halley’s method without second derivative with two parameters. Methodology: In order to avoid the second derivative, it is approximated by using an equality of two methods, namely, use of a circle of curvature that has the same tangent line and to equate to the Potra-Ptak’s method. Results: The results show that the method requires two evaluation of functions and one its first derivative per iteration with the efficiency index equal to 4^⅓ ≈ 1.5874. The convergence analysis shows that the proposed method has the fourth-order convergence for θ = 1 and β = 1 and requires three evaluation of functions per iteration. Conclusion: The final results show that the proposed methods has better performance as compared some other kind of methods. A numerical simulation is presented to show the performance of the proposed method by using several functions.

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