On generalized one-step derivative-free iterative family for evaluating multiple roots

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 17 آبان 1402

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2023.82958.1282

نویسندگان

Himani Arora¹؛ Alicia Codero^{* 2}؛ Juan R. Torregrosa²

¹Department of Mathematics, Guru Nanak Dev University, 143005, Amritsar, India

²Instituto de Matem`atica Multidisciplinar, Universitat Polit`ecnica de Val`encia, 46022, Valencia, Spain.

چکیده

In this study, we propose a family of iterative procedures with no derivatives for calculating multiple roots of one-variable nonlinear equations. We also present an iterative technique to approximate the multiplicity of the roots. The new class is optimal since it fits the Kung-Traub hypothesis and has second-order convergence. Derivative-free methods for calculating multiple roots are rarely found in literature, especially in the case of one-step methods, which are the simplest ones in terms of their structure. Moreover, this new family contains almost all the existing single-step derivative-free iterative schemes as its special cases, with an additional degree of freedom. Several results are used to confirm its theoretical order of convergence. Through the complex discrete dynamics analysis, the stability of the suggested class is illustrated and the most stable methods are found. Several test problems are included to check the performance of the proposed methods, whether the multiplicity of the roots is estimated or known, comparing the numerical results with those obtained by other methods.

کلیدواژه‌ها

Nonlinear equations؛ Derivative-free iterative method؛ Multiple roots؛ Order of convergence؛ Stability