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

Supriadi Putra (Department of Mathematics, University of Riau, Pekanbaru 28293, Indonesia)
M Imran (Department of Mathematics, University of Riau, Pekanbaru 28293, Indonesia)
Ayunda Putri (Department of Mathematics, University of Riau, Pekanbaru 28293, Indonesia)
Rike Marjulisa (Department of Mathematics, University of Riau, Pekanbaru 28293, Indonesia)

International Journal of Quantitative Research and Modeling
Vol. 4 No. 4 (2023): International Journal of Quantitative Research and Modeling

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.