In this manuscript, we design an efficient sixth-order scheme for solving nonlinear systems of equations, with only two steps in its iterative expression. Moreover, it belongs to a new parametric class of methods whose order of convergence is, at least, four. In this family, the most stable members have been selected by using techniques of real multidimensional dynamics; also, some members with undesirable chaotic behavior have been found and rejected for practical purposes. Finally, all these high-order schemes have been numerically checked and compared with other existing procedures of the same order of convergence, showing good and stable performance.

在此手稿中，我们设计了一种有效的六阶方案，用于求解方程组的非线性系统，其迭代表达式只有两个步骤。而且，它属于一种新的参数化方法类，其收敛阶至少为4。在这个家族中，最稳定的成员是通过使用真实的多维动力学技术来选择的。另外，出于实际目的，发现并拒绝了一些具有不良混沌行为的成员。最后，所有这些高阶方案都经过了数值检验，并与其他具有相同收敛阶数的过程进行了比较，显示了良好且稳定的性能。