International Journal of Pure and Applied Mathematics Volume 110 No. 1 2016, 1-7 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu doi: 10.12732/ijpam.v110i1.1 P A ijpam.eu A NEW FAMILY OF SECANT-LIKE METHOD WITH SUPER-LINEAR CONVERGENCE M. Imran 1 § , Syamsudhuha 2 , Supriadi Putra 3 1,2,3 Numerical Computing Group Department of Mathematics University of Riau Pekanbaru, 28293, INDONESIA Abstract: Another new family of Secant-like method is proposed in this paper. Analysis of convergence shows that the method has a super-linear convergence as Secant method. Numerical experiments show that the efficiency of the method is depended on the value of its parameter. AMS Subject Classification: 65D99, 65H05 Key Words: secant-like method, secant method, order of convergence, iterative method 1. Introduction In this study, we are concerned of finding an approximated solution of a non- linear equation of the form f (x)=0. (1) A classic known method without employing derivative to solve (1) is Se- cant method derived by passing a line through two point, says (x 0 ,f (x 0 )) and (x 1 ,f (x 1 )). The equation of this line is p(x)= f (x 1 )+ f (x 1 ) − f (x 0 ) x 1 − x 0 (x − x 1 ). (2) The intersection of (2) with x-axis is the first approximation to the root of Received: October 29, 2015 Revised: August 31, 2016 Published: October 21, 2016 c  2016 Academic Publications, Ltd. url: www.acadpubl.eu § Correspondence author