An optimal eighth order derivative free multiple root finding numerical method and applications to chemistry

[EN] In this paper, we present an optimal eighth order derivative-free family of methods for multiple roots which is based on the first order divided difference and weight functions. This iterative method is a three step method with the first step as Traub-Steffensen iteration and the next two taken as Traub-Steffensen-like iteration with four functional evaluations per iteration. We compare our proposed method with the recent derivative-free methods using some chemical engineering problems modelled as nonlinear equations with simple and multiple roots. Stability of the presented family of methods is demonstrated by using the graphical tool known as basins of attraction. ; Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. ; Cordero Barbero, A.; Fiza Zafar; Ifra Ashraf; Torregrosa Sánchez, JR. (2023). An optimal eighth order derivative free multiple root finding numerical method and applications to chemistry. Journal of Mathematical Chemistry (Online). 61(1):98-124. https://doi.org/10.1007/s10910-022-01411-1 ; 98 ; 124 ; 61 ; 1