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A new family of Newton-type methods with 4m order of convergence for solving nonlinear equations

R. Thukral


In this paper, we derive new Newton-type iterative methods with 4m order of convergence for solution of nonlinear equations. Method of different order of convergence is constructed using a suitable parametric function and an arbitrary real parameter. We have proved that the Newton-type methods have the convergence order 4m for some values of m. In addition, we have found a simple formula to calculate the asymptotic error constant of these new methods. Consequently, we have examined the effectiveness of the new Newton-type methods by approximating the simple root of a given nonlinear equation. Numerical example is given to demonstrate the performance of these new methods.


Newton-type methods; Nonlinear equations; Iterative methods; Asymptotic error constant; Order of convergence.

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