ICCM Conferences, The 8th International Conference on Computational Methods (ICCM2017)

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An optimal eighth-order scheme for multiple zeros of univariate functions
Ramandeep Behl, Fiza Zafar, Ali Saleh Alshomrani, Moin-ud-din Junjua, Nusrat Yasmin

Last modified: 2017-09-26


We present an optimal eighth-order scheme which will work for multiple zeros with multiplicity (m>1), for the first time. Earlier, the maximum convergence order of multi-point iterative schemes was six for multiple zeros in the available literature. So, the main contribution of this study is to present a new higher-order and as well as an optimal scheme for multiple zeros for the first time. In addition, we present an extensive convergence analysis with the main theorem which confirms theoretically eighth-order convergence of the presented scheme. Moreover, we consider several real life problems which contain simple as well as multiple zeros in order to comparison with the existing robust iterative schemes. Finally, we conclude on the basis of obtained numerical results that the proposed iterative methods perform far better than the existing methods in terms of residual error, computational order of convergence and difference between the two consecutive iterations.


Nonlinear equations; Kung-Traub conjecture; multiple zeros; efficiency index; optimal iterative methods

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