Abstract
The goal of this paper is to study a classic problem used in several fields such as science and engeneering. It’s solving nonlinear equations: f (x) = 0; where f : R → R is considered of class C^1 on the interval I containing x^* the solution of (1) .
 We propose in this research a new method for solving nonlinear equations. A convergence acceleration result is established and numerical examples are given.
Highlights
Nonlinear equations are widely used to mathematically model many scientific computing problems
We propose in this research a new method for solving nonlinear equations
It is easy to see that the approximation defined by hybrid procedures will be given by: xn+1
Summary
Nonlinear equations are widely used to mathematically model many scientific computing problems. Our objective is to use hybrid procedures (Brezinski & Chehab, 1998) to build a method whose convergence is at least quadratic, without computing the derivative for each iteration. Chehab in (Brezinski & Chehab, 1998) for solving fixed point problems. Let x′ and x′′ be two approximate solutions for the equation (1), hybrid procedures construct a new approximate solution y defined by: y αx”. It is easy to see that the approximation defined by hybrid procedures will be given by: xn h f (xn f (xn) h f (xn))
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