This study suggests a new general scheme of high convergence order for approximating the solutions of nonlinear systems. The proposed scheme is the extension of an earlier study of Parhi and Gupta. This method requires two vector-function, two Jacobian matrices, two inverse matrices, and one frozen inverse matrix per iteration. Convergence error, computational efficiency, and numerical experiments are performed to verify the applicability and validity of the proposed methods compared with existing methods. Finally, we discuss the strange fixed points and conjugacy functions on a particular case of our scheme. The basins of attractions also demonstrate the dynamical behavior of this special case in the neighborhood of required roots and also assert the theoretical outcomes.

这项研究提出了一种高收敛阶的新通用方案，用于近似非线性系统的解。提议的方案是对Parhi和Gupta的早期研究的扩展。此方法每次迭代需要两个向量函数，两个Jacobian矩阵，两个逆矩阵和一个冻结逆矩阵。进行了收敛误差，计算效率和数值实验，以验证所提方法与现有方法的适用性和有效性。最后，我们讨论该方案的特定情况下的奇怪的不动点和共轭函数。吸引力盆地也证明了这种特殊情况在必需根附近的动力学行为，并证明了理论结果。