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Publication Type : Journal Article
Source : International Journal of Nonlinear Sciences and Numerical Simulation (2021), doi.org/10.1515/ijnsns-2020-0161.
Url : https://www.degruyter.com/document/doi/10.1515/ijnsns-2020-0161/html?lang=en
Campus : Chennai
School : School of Engineering
Department : Mathematics
Year : 2021
Abstract : Many optimal order multiple root techniques, which use derivatives in the algorithm, have been proposed in literature. Many researchers tried to construct an optimal family of derivative-free methods for multiple roots, but they did not get success in this direction. With this as a motivation factor, here, we present a new optimal class of derivative-free methods for obtaining multiple roots of nonlinear functions. This procedure involves Traub–Steffensen iteration in the first step and Traub–Steffensen-like iteration in the second step. Efficacy is checked on a good number of relevant numerical problems that verifies the efficient convergent nature of the new methods. Moreover, we find that the new derivative-free methods are just as competent as the other existing robust methods that use derivatives.
Cite this Research Publication : Sunil Kumar, Deepak Kumar, Janak Raj Sharma, Ioannis K. Argyros “An efficient class of fourth-order derivative free method for multiple roots”, International Journal of Nonlinear Sciences and Numerical Simulation (2021), doi.org/10.1515/ijnsns-2020-0161.