This paper presents a fifth-order iterative method as a new modification of Newton's method for finding multiple roots of nonlinear equations with unknown multiplicity m. Its convergence order is analyzed and proved. Moreover, several numerical examples demonstrate that the proposed iterative method is superior to the existing methods.
Keywords Nonlinear equation · Multiple roots · Newton-like method · High-order convergence · Iterative methodsWe consider the iterative method to solve multiple roots x * of a nonlinear equation f 0 (x) = 0, where f 0 : [a, b] ⊂ R → R is a nonlinear differential function on [a, b]. Schröder [1] has modified Newton's method to obtain a multiple root when the multiplicity m is known
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