Kong-ied, Butsakorn Two new eighth- and twelfth-order iterative methods for solving nonlinear equations. (English) Zbl 1450.65045 Int. J. Math. Comput. Sci. 16, No. 1, 333-344 (2021). Summary: In this paper, we present two new iteration methods to find the solutions of nonlinear equations, which were developed from a concept of [O. Said Solaiman and I. Hashim, Math. Probl. Eng. 2019, Article ID 1728965, 11 p. (2019; Zbl 1435.65075)] and Taylor’s series to estimate the second derivative with convergence order analysis of the two new methods. The new methods have eight-order convergence with the efficiency index at \((8)^{\frac{1}{3}}\approx 1.5157\), and twelfth-order convergence with the efficiency index at \((12)^{\frac{1}{6}}\approx 1.5131\). Numerical examples of the new methods are compared with other methods by exhibiting the effectiveness of the method presented in this paper. MSC: 65H20 Global methods, including homotopy approaches to the numerical solution of nonlinear equations Keywords:nonlinear equations; Newton’s method; order of convergence Citations:Zbl 1435.65075 PDFBibTeX XMLCite \textit{B. Kong-ied}, Int. J. Math. Comput. Sci. 16, No. 1, 333--344 (2021; Zbl 1450.65045) Full Text: Link