An efficient high order iterative scheme for large nonlinear systems with dynamics

Abstract This study suggests a new general scheme of high convergence order for approximating the solutions of nonlinear systems. The proposed scheme is the extension of an earlier study of Parhi and Gupta. This method requires two vector-function, two Jacobian matrices, two inverse matrices, and one frozen inverse matrix per iteration. Convergence error, computational efficiency, and numerical experiments are performed to verify the applicability and validity of the proposed methods compared with existing methods. Finally, we discuss the strange fixed points and conjugacy functions on a particular case of our scheme. The basins of attractions also demonstrate the dynamical behavior of this special case in the neighborhood of required roots and also assert the theoretical outcomes.