Design of new derivative-free iterative methods with memory for solving system of nonlinear equations

In the present article, we introduce derivative-free methods with memory that exhibit increasing convergence orders for solving systems of nonlinear equations. These with-memory methods are built upon the existing fourth-order method without memory by adjusting four different free self-corrected parameters in each iterative step. The convergence order of the new methods with memory is enhanced from 4 to approximately 4.23607, 4.44949, 4.56155 and 5.23607. The computational efficiency of the proposed techniques is also examined over well existing similar nature methods. It is demonstrated that these new methods generally offer greater efficiency and a conclusion is supported by numerical experiments.