We introduce here a new two-step derivate-free inverse simultaneous iterative method for estimating all roots of nonlinear equation. It is proved that convergence order of the newly constructed method is four. Lower bound of the convergence order is determined using Mathematica and verified with theoretical local convergence order of the method introduced. Some nonlinear models which are taken from physical and engineering sciences as numerical test examples to demonstrate the performance and efficiency of the newly constructed modified inverse simultaneous methods as compared to classical methods existing in literature are presented. Dynamical planes and residual graphs are drawn using MATLAB to elaborate efficiency, robustness, and authentication in its domain.

中文翻译：

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求解非线性方程所有根的逆数值迭代技术及其工程应用

我们在这里介绍了一种新的两步无导数逆同时迭代方法，用于估计非线性方程的所有根。证明了该新方法的收敛阶为四。使用Mathematica确定收敛阶的下界，并用所介绍方法的理论局部收敛阶进行验证。提出了一些非线性模型，这些模型是从物理和工程科学中作为数值测试示例，以证明与文献中存在的经典方法相比，新构造的改进的逆同时方法的性能和效率。使用MATLAB绘制动力学平面和残差图，以详细说明其领域中的效率，鲁棒性和身份验证。