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Discrete Dynamics in Nature and Society
Volume 2015, Article ID 938606, 7 pages
Research Article

Two Bi-Accelerator Improved with Memory Schemes for Solving Nonlinear Equations

Department of Mathematics, Maulana Azad National Institute of Technology, Bhopal, Madhya Pradesh 462051, India

Received 16 October 2014; Accepted 27 December 2014

Academic Editor: Giuseppe Izzo

Copyright © 2015 J. P. Jaiswal. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The present paper is devoted to the improvement of the -order convergence of with memory derivative free methods presented by Lotfi et al. (2014) without doing any new evaluation. To achieve this aim one more self-accelerating parameter is inserted, which is calculated with the help of Newton’s interpolatory polynomial. First theoretically it is proved that the -order of convergence of the proposed schemes is increased from 6 to 7 and 12 to 14, respectively, without adding any extra evaluation. Smooth as well as nonsmooth examples are discussed to confirm theoretical result and superiority of the proposed schemes.