A Novel Family of Multiple Root Finders with Optimal Eighth-Order Convergence and their Basins of Attraction
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Date
2024
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International Conference of Numerical Analysis and Applied Mathematics AIP Conf. Proc.
Abstract
In this contribution, a novel scheme of multiple root finders for nonlinear equations with the univariate and bivariate
weight functions is proposed. The basic requirement of the presented scheme is the known value of ’m’ (multiplicity of the root).
Analysis of convergence is given to show that the proposed family achieves eighth-order convergence. Numerical experimentation
is done to demonstrate accuracy and computational efficiency of the scheme. In addition, the obtained results show that the
proposed scheme has an edge-over other considered eighth-order methods