An Improved R-order Convergence Derivative-Free Method for Solving Nonlinear Equations

In this paper an improved bi-parametric self-accelerating family of three-point derivative free methods for solving nonlinear equa- tions with memory is presented. Self-accelerating parameters are calculated by Newton's interpolatory polynomial of degree four and five. The importance of imposing two parameters is that they accelerated the R-order convergence of the existing method from 12 to 14 without any additional evaluations. Finally, numerical examples and comparisons are included to confirm the theoretical result and high computational efficiency.