The principle aim of this manuscript is to introduce a new highly efficient improved modification of Chebyshev–Halley family with increasing order of convergence. The idea is based on the schemes proposed by Li et al. (Appl Math Comput 235:221–225, 2014) and Sharma (Appl Math Comput 256:119–124, 2015). The proposed scheme has at least seventh-order of convergence and also posses an optimal eighth-order of convergence for a particular value of the disposable parameter. Each member of the proposed scheme is free from second-order derivative and requires only four functional evaluations (viz. three evaluations of function f and one of first-order derivative $$f'$$ f ′ ) per full iteration. A variety of concrete numerical examples demonstrates that our proposed scheme performs better than the existing schemes proposed by Li et al. (Appl Math Comput 235:221–225, 2014) and Sharma (Appl Math Comput 256:119–124, 2015). Dynamical study of our methods also confirms the above conclusions to a great extent. Moreover, the local convergence of these methods is given using hypotheses only on the first derivative and Lipschitz constants.
SeMA Journal – Springer Journals
Published: Jan 16, 2017
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