Higher order derivative-free iterative methods with and without memory for systems of nonlinear equations

A derivative-free family of iterations without memory consisting of three steps for solving nonlinear systems of equations is brought forward. Then, the main aim of the paper is furnished by proposing several novel schemes with memory possessing higher rates of convergence. Analytical discussions are reported and the theoretical efficiency of the methods is studied. Application of the schemes in solving partial differential equations is finally provided to support the theoretical discussions.