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Two new eighth- and twelfth-order iterative methods for solving nonlinear equations. (English) Zbl 1450.65045

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

Citations:

Zbl 1435.65075
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