Variant of Trapezoidal-Newton Method for Solving Nonlinear Equations and its Dynamics

Supriadi Putra; M Imran; Ayunda Putri; Rike Marjulisa

doi:10.46336/ijqrm.v4i4.539

Variant of Trapezoidal-Newton Method for Solving Nonlinear Equations and its Dynamics

Supriadi Putra, M Imran, Ayunda Putri, Rike Marjulisa

Abstract

This article introduces a novel approach resulting from the adaptation of Trapezoidal-Newton method variants. The iterative process is enhanced through the incorporation of a numerical integral strategy derived from two-partition Trapezoidal method. Through rigorous error analysis, the study establishes a third order convergence for this method. It emerges as a viable alternative for solving nonlinear equations, a conclusion substantiated by computational costs conducted on diverse nonlinear equation forms. Furthermore, an exploration of basin of attraction analyses that this method exhibits faster convergence compared to other Newton-type methods, albeit with a slightly expanded divergent region with a variant of Newton Simpson’s method.

Keywords

basins of attraction, nonlinear equation, Trapezoidal-Newton variant methods, Newton-Simpson variant methods

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DOI: https://doi.org/10.46336/ijqrm.v4i4.539