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Ball Convergence of Multipoint Methods for Non-linear Systems
(Springer Science and Business Media Deutschland GmbH, 2021) Argyros, I.K.; George, S.; Erappa, S.M.
We study Multipoint methods using only the first derivative. Earlier studies use higher than three order derivatives not on the methods. Moreover Lipschitz constants are used to find error estimates not presented in earlier papers. Numerical examples complete this paper. Â© 2021, Springer Nature Singapore Pte Ltd.
Local convergence of a novel eighth order method under hypotheses only on the first derivative
(Tusi Mathematical Research Group (TMRG) moslehian@memeber.ams.org, 2019) Argyros, I.K.; George, S.; Erappa, S.M.
We expand the applicability of eighth order-iterative method stud- ied by Jaiswal in order to approximate a locally unique solution of an equation in Banach space setting. We provide a local convergence analysis using only hypotheses on the first Frechet-derivative. Moreover, we provide computable convergence radii, error bounds, and uniqueness results. Numerical examples computing the radii of the convergence balls as well as examples where earlier results cannot apply to solve equations but our results can apply are also given in this study. © 2019 Khayyam Journal of Mathematics.