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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 105
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Paper 37

A New 'With' Memory Method using Two Accelerators

T. Lotfi and K. Mahdidni

Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran

Full Bibliographic Reference for this paper
T. Lotfi, K. Mahdidni, "A New 'With' Memory Method using Two Accelerators", in , (Editors), "Proceedings of the Ninth International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 37, 2014. doi:10.4203/ccp.105.37
Keywords: nonlinear equations, iterative methods, multipoint methods, without memory methods, with memory methods, Kung and Traub's conjecture, efficiency index.

In this work, we attempt to develop a new and efficient two-point with memory method to estimate simple roots of a given nonlinear equation. To this end, first, we consider an optimal two-point method without memory in which it uses only three functional evaluations per iteration having convergence order four. Applying two accelerator parameters in each iteration, we try to increase the convergence order from four to seven without any new extra function evaluations. We call it with memory method. Consequently, the efficiency index of the optimal two-point without memory method is increased from 41/3~1.58 to 71/3~1.91 which is better than an optimal five-step (or six-point) without memory with efficiency index equal to 321/6~1.78

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