A new optimal iterative algorithm for solving nonlinear equations
Abstract
The aim of this paper is to propose a new iterative algorithm (scheme or method) for solving algebraic and transcendental equations, considering a fixed point and an initial guess value on the x-axis. The concepts of the slope of a line and the Taylor series are used in the derivation. The algorithm has second-order convergence and requires two function evaluations in each step, which shows that it is optimal with a computational efficiency index of 1.414 and an informational efficiency of 1. The validity of the algorithm is examined by solving some examples and their comparisons with Newton’s method.
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