In this paper, a new fourth-order iterative scheme for finding the zeros of systems of nonlinear equations has been built and analyzed. Theoretical proof has been given to confirm the convergence order of the new method. The effectiveness of the proposed method is shown by the comparison of traditional as well as flops-like efficiency index with recent existing same order schemes. Numerical examples confirm that the new iterative method is efficient and gives tough competition to some existing fourth-order methods. We have also discussed the application of our proposed method for finding numerical solution of nonlinear ODE and PDE.

中文翻译：

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计算非线性方程组数值解的三步有效四阶方法及其应用

本文建立并分析了一种新的四阶迭代方案，用于寻找非线性方程组的零点。理论证明已经证实了该方法的收敛顺序。通过将传统以及类似触发器的效率指数与最近存在的相同阶数方案进行比较，表明了该方法的有效性。数值算例表明，新的迭代方法是有效的，并且与某些现有的四阶方法产生了激烈的竞争。我们还讨论了我们提出的方法在寻找非线性ODE和PDE数值解时的应用。