We suggest a new high-order family of iterative schemes for obtaining the solutions of nonlinear systems. The present scheme is an improvisation and extension of classical Chebyshev–Halley family for nonlinear systems along with higher-order convergence than the original scheme. The main theorem verifies the theoretical convergence order of our scheme along with convergence properties. In order to demonstrate the suitability of our technique, we choose several real life and academic test problems namely, boundary value, Bratu’s 2D, Fisher’s problems and some nonlinear system of minimum order of $$150\times 150$$ 150 × 150 of nonlinear equations, etc. Finally, we wind up on the ground of computational consequences that our iterative methods demonstrate better performance than the existing schemes with respect to absolute residual errors, the absolute errors among two consecutive estimations and stable computational convergence order.

中文翻译：

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非线性方程组的一个有效的 Chebyshev-Halley 方法族

我们建议使用一个新的高阶迭代方案族来获得非线性系统的解。本方案是非线性系统经典 Chebyshev-Halley 族的即兴和扩展，以及比原始方案更高阶的收敛性。主要定理验证了我们方案的理论收敛顺序以及收敛特性。为了证明我们的技术的适用性，我们选择了几个现实生活和学术测试问题，即边界值、Bratu's 2D、Fisher's 问题和一些最小阶数为 $$150\times 150$$ 150 × 150 的非线性方程的非线性系统最后，我们基于计算结果得出结论，我们的迭代方法在绝对残差方面表现出比现有方案更好的性能，