A derivative-free iterative method of convergence order five for solving systems of nonlinear equations is presented. The computational efficiency is examined and the comparison between efficiencies of the proposed technique with existing most efficient techniques is performed. It is shown that the new method has less computational cost than the existing counterparts, which implies that the method is computationally more efficient. Numerical problems, including those resulting from discretization of boundary value problem and integral equation, are given to compare the performance of the proposed method with existing methods and to confirm the theoretical results concerning the order of convergence and efficiency. The numerical results, including the elapsed CPU time, confirm the accurate and efficient character of the proposed technique.

中文翻译：

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非线性系统的降低成本的无导数高阶数值算法

提出了一种求解非线性方程组的收敛性为五阶的无导数迭代方法。检查了计算效率，并比较了所提出技术与现有最有效技术的效率。结果表明，该新方法比现有方法具有更低的计算成本，这表明该方法在计算效率上更高。给出了数值问题，包括由离散化边值问题和积分方程引起的数值问题，以比较该方法与现有方法的性能，并确认有关收敛顺序和效率的理论结果。包括经过的CPU时间在内的数值结果证实了所提出技术的准确和高效特性。