<![CDATA[This article discusses the families of Newton-Like methods derived from a combination of the secant method with Newton’s method based on the trapezoidal rule and inverse function to find a root of nonlinear equations. Analytically, it is shown that the iterative methods have the order of convergence four and for each iteration, they require four function evaluations, so the efficiency index is 1.414 which is the same as Newton’s method. Furthermore, computational results show that the iterative method is superior to the comparison methods in terms of the number of iterationsto obtain the estimated roots.]]>
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