CMMSE: A novel scheme having seventh-order convergence for nonlinear systems

Abstract

In this paper, we present a new three-point iterative scheme for obtaining the solution of nonlinear system having seventh-order convergence. The beauty of our scheme is that we obtained the seventh-order convergence with minimal computational cost as compared to the existing ones. In addition, we also analyze the theoretical convergence properties of the proposed scheme. Moreover, we show its applicability on a total six numbers of nonlinear models: first three of them are boundary value, Hammerstein integral and 2D Bratu’s problems; the last three are standard academic large systems of nonlinear equations of order 50 × 50, 100 × 100 and 120 × 120, respectively. Finally, we concluded on the basis of obtained numerical experiments that our iterative method performs better in terms of residual error, computational efficiency, error between the two consecutive iterations, CPU-time, asymptotic error constant term and approximated root.