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Keywords:
nonlinear system; iteration method; optimal order; computational efficiency; convergence plane
nonlinear system; iteration method; optimal order; computational efficiency; convergence plane
Summary:
We generalize an optimal fourth-order scalar method to solve systems of nonlinear equations. The proposed generalized scheme is optimal for solving systems of nonlinear equations. The fourth-order convergence of the proposed method is proved. The computational efficiency of the proposed iteration scheme is analysed and compared with several methods for nonlinear systems. To evaluate the numerical performance of the presented scheme, extensive numerical experiments are conducted and the results are compared with some existing fourth-order methods from the literature. The stability of the scheme is rigorously analysed through convergence planes, confirming its advantage over other fourth-order iteration techniques for systems of nonlinear equations.
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