Journal of Advances in Applied Mathematics

Download PDF (407.7 KB) PP. 203 - 210 Pub. Date: October 1, 2016

DOI: 10.22606/jaam.2016.14001

• J. P. Jaiswal^*
  Department of Mathematics, Maulana Azad National Institute of Technology, Bhopal, M.P., India-462003

The present paper is devoted to the improvement of the existing fourth-and eighth-order derivative free methods without memory proposed by Cordero et al. (2013). To achieve this goal two parameters are introduced which are calculated with the help of Newton’s interpolatory polynomial. It is shown that the R-order convergence of the proposed methods has been increased from 4 to 7 and 8 to 14, respectively without any extra evaluation.Two non-smooth examples are demonstrated to confirm theoretical results. Numerically the modified methods are examined along with comparison to recent existing with memory methods.

Derivative free method, nonlinear equations, order of convergence, efficiency index, nonsmooth function.

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