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

• DOI: 10.1007/s10910-022-01411-1
• Publication Date: 2022-10-21T06:04:22Z
• Authors: Fiza Zafar; Alicia Cordero; Ifra Ashraf; Juan R. Torregrosa
• Keywords: Derivative (finance); Mathematical chemistry; Root (linguistics)

Abstract In this paper, we present an optimal eighth order derivative-free family of methods for multiple roots which is based on the first divided difference and weight functions. This iterative method a three step with as Traub–Steffensen iteration next two taken Traub–Steffensen-like four functional evaluations per iteration. We compare our proposed recent using some chemical engineering problems modelled nonlinear equations simple roots. Stability presented demonstrated by graphical tool known basins attraction.