Improved bi-accelerator derivative free with memory family for solving nonlinear equations

The object of the present paper is to accelerate the $R$-order convergence of with memory derivative free family given by Lotfi et al. (2014) without adding any new evaluations. To achieve this goal one more iterative parameter is introduced, which is calculated with the help of Newton''s interpolatory polynomial. It is shown that the $R$-order convergence of the proposed scheme is increased from 12 to 14 without any extra evaluation. Smooth as well as non-smooth examples are presented to confirm theoretical result and significance of the new scheme.