Some modifications and extensions of Popovski’s and Laguerre’s families for solving systems of nonlinear equations

Two modifications of Popovski’s and Laguerre’s families of methods are developed, which free of second derivatives. The improved modifications have fourth-order of convergence. Moreover, we propose the extensions of modifications to solve nonlinear systems. The convergence order of two and three-step iterations equal to four, six and seven respectively. The numerical results confirm the order of convergence. In addition, we investigate the basin of attraction of the methods and its dependence on the convergence behavior. The comparison is made based on the performance on examples of nonlinear problems and the CPU time.