In this piece of research, cubic and quartic Hyperbolic B-splines based Differential quadrature methods are implemented for numerical approximation of coupled 2 and 3 Navier-Stokes equations. The validity of the proposed regimes is tested by the means of different variety of errors such as; error, error, error, and error. It is noticed that most of the time, errors generated by cubic Hyperbolic B-spline are far better than those of quartic Hyperbolic B-spline. Numerical convergence of the Method I is also validated in this research. The main key aspect of this research is the fusion of numerical simulation and statistical analysis. The data generated vis the considered error. Thereafter, on the basis of fetched errors, correlation matrix heatmaps are provided claiming the types of correlation occurred between mentioned parameters and errors. This research work is not only important from Mathematical aspect but also it will be a major breakthrough in the field of Statistics. This study's primary contribution is the assertion that numerical methods based on cubic hyperbolic B-spline are more efficient than quartic order methods. Furthermore, another distinguishing feature of this work is the incorporation of statistical concepts as correlation in such studies.

中文翻译：

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通过微分求积法对耦合纳维斯托克斯方程进行三次和四次双曲 B 样条比较 - 统计方面


在这项研究中，基于微分求积方法的三次和四次双曲 B 样条被实现用于耦合 2 和 3 纳维-斯托克斯方程的数值近似。所提出的制度的有效性是通过不同种类的错误来测试的，例如：错误，错误，错误，还是错误。值得注意的是，大多数时候，三次双曲B样条产生的误差远远好于四次双曲B样条。本研究也验证了方法一的数值收敛性。这项研究的主要关键方面是数值模拟和统计分析的融合。生成的数据与所考虑的错误。此后，根据获取的错误，提供相关矩阵热图，声明上述参数和错误之间发生的相关类型。这项研究工作不仅在数学方面具有重要意义，而且将是统计学领域的重大突破。这项研究的主要贡献是断言基于三次双曲 B 样条的数值方法比四次阶方法更有效。此外，这项工作的另一个显着特征是将统计概念作为相关性纳入此类研究中。