An efficient family of Chebyshev–Halley’s methods for system of nonlinear equations

Abstract

We suggest a new high-order family of iterative schemes for obtaining the solutions of nonlinear systems. The present scheme is an improvisation and extension of classical Chebyshev–Halley family for nonlinear systems along with higher-order convergence than the original scheme. The main theorem verifies the theoretical convergence order of our scheme along with convergence properties. In order to demonstrate the suitability of our technique, we choose several real life and academic test problems namely, boundary value, Bratu’s 2D, Fisher’s problems and some nonlinear system of minimum order of $$150\times 150$$ of nonlinear equations, etc. Finally, we wind up on the ground of computational consequences that our iterative methods demonstrate better performance than the existing schemes with respect to absolute residual errors, the absolute errors among two consecutive estimations and stable computational convergence order.