An efficient class of fourth-order derivative-free method for multiple-roots
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Sunil Kumar
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Janak Raj Sharma
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.
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Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: No funding.
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Conflict of interest statement: There is no conflict of interest.
References
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- Unsteady MHD natural convection flow of a nanofluid inside an inclined square cavity containing a heated circular obstacle
- Fractional-order generalized Legendre wavelets and their applications to fractional Riccati differential equations
- Battery discharging model on fractal time sets
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