In this paper, we propose two novel iteration schemes for computing zeros of nonlinear equations in one dimension. We develop these iteration schemes with the help of Taylor’s series expansion, generalized Newton-Raphson’s method, and interpolation technique. The convergence analysis of the proposed iteration schemes is discussed. It is established that the newly developed iteration schemes have sixth order of convergence. Several numerical examples have been solved to illustrate the applicability and validity of the suggested schemes. These problems also include some real-life applications associated with the chemical and civil engineering such as adiabatic flame temperature equation, conversion of nitrogen-hydrogen feed to ammonia, the van der Wall’s equation, and the open channel flow problem whose numerical results prove the better efficiency of these methods as compared to other well-known existing iterative methods of the same kind.

中文翻译：

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计算非线性标量方程零点的一些新颖的六阶迭代方案及其在工程中的应用

在本文中，我们提出了两种新颖的迭代方案，用于在一维中计算非线性方程的零点。我们借助泰勒级数展开，广义牛顿-拉夫森方法和插值技术来开发这些迭代方案。讨论了所提出的迭代方案的收敛性分析。可以确定的是，新开发的迭代方案具有六阶收敛性。解决了几个数值示例，以说明所建议方案的适用性和有效性。这些问题还包括与化学和土木工程相关的一些实际应用，例如绝热火焰温度方程，氮氢进料到氨的转化，范德华尔方程，