Convergence and Dynamics of Schröder’s Method for Zeros of Analytic Functions with Unknown Multiplicity

Plamena I. Marcheva and Stoil I. Ivanov ()
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Plamena I. Marcheva: Faculty of Physics and Technology, University of Plovdiv Paisii Hilendarski, 24 Tzar Asen, 4000 Plovdiv, Bulgaria
Stoil I. Ivanov: Faculty of Physics and Technology, University of Plovdiv Paisii Hilendarski, 24 Tzar Asen, 4000 Plovdiv, Bulgaria

Mathematics, 2025, vol. 13, issue 2, 1-13

Abstract: In this paper, we investigate the local convergence of Schröder’s method for finding zeros of analytic functions with unknown multiplicity. Thus, we obtain a convergence theorem that provides exact domains of initial points together with error estimates to ensure the Q -quadratic convergence of Schröder’s method right from the first step. A comparison with the famous Newton’s method, based on the convergence and dynamics when it is applied to some polynomial and non-polynomial equations, is also provided.

Keywords: iteration methods; Schröder’s method; local convergence; analytic functions; basins of attraction; multiple zeros; error estimates (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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