Further development of secant-type methods for solving nonlinear equations -by R. Thukral

# Further development of secant-type methods for solving nonlinear equations-by R. Thukral

Abstract: The objective of this paper is to define new improved Secant-type methods for finding simple root of nonlinear equations. In terms of computational cost the new iterative methods requires two evaluations of functions per iteration. It is shown and proved that the new methods have a convergence of order $1+\sqrt{3}$. Numerical comparisons are made to demonstrate exceptional convergence speed of the proposed methods. It is observed that the new iterative methods are very competitive with the similar robust methods.

Keywords: Secant-type methods; Newton method; Simple root; Nonlinear equations; Root-finding; Order of convergence.