In this study, a numerical technique is applied to investigate solutions of linear variable order differential equations(VODEs) in fluid mechanics. We investigate variable order(VO) in the Caputo sense. Our aim is to apply Bernstein polynomials(Bps) as the basis functions and operational matrices. We calculate two types of operational matrices of Bps. Using these operational matrices the main equation can be transformed into a system of algebraic equations, which must then be solved to get approximate solutions. Some examples are provided to indicate the accuracy of the presented method.

中文翻译：

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一种使用伯恩斯坦多项式求解变量微分方程的数值方法

在这项研究中，数值技术被应用于研究流体力学中的线性可变阶微分方程（VODEs）的解。我们从Caputo的意义上研究可变阶（VO）。我们的目标是将伯恩斯坦多项式（Bps）用作基本函数和运算矩阵。我们计算了Bps的两种运算矩阵。使用这些运算矩阵，主方程可以转换为代数方程组，然后必须对其进行求解以获得近似解。提供一些示例以表明所提出方法的准确性。