Seventh-order derivative-free iterative method for solving nonlinear systems

In this paper, a multi-step iterative method with seventh-order local convergence is presented, for solving nonlinear systems. A development of an inverse first-order divided difference operator for multivariable function is applied to prove the local convergence order of the new method. The computational efficiency is compared with some known methods. It is proved that the new method is more efficient. Numerical experiments are performed, which support the theoretical results. From the comparison with some known methods it is observed that the new method remarkably saves the computational time in the high-precision computing.

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