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A New Third-Order Iterative Method for Solving Nonlinear Equations with Multiple Roots

R. Thukral


A new method of order three for finding multiple zeros of nonlinear equations is developed. Per iteration the new method requires two evaluations of the function and one evaluation of its first derivative. We shall examine the effectiveness of the new third-order Newton-type method by approximating the multiple roots of a given nonlinear equation. The estimate of the multiple root of a nonlinear equation using the new method is found to be substantially more accurate than the established third-order methods.


Modified Newton method, Newton-type method, Nonlinear equations, Multiple roots, Order of convergence

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