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

Abstract EN

The present paper is devoted to the improvement of the R-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 R-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.