The Bernstein operators (BO) are not orthogonal, but they have duals, which are obtained by a linear combination of BO. In recent years dual BO have been adopted in computer graphics, computer aided geometric design, and numerical analysis. This paper presents a numerical method based on the Bernstein operational matrices to solve the time–space fractional convection–diffusion equation. A generalization of the derivative matrix operator of fractional order and the error analysis are discussed. Numerical examples compare the proposed approach with previous works, showing that the method is more accurate and efficient.

中文翻译：

---

地下水污染中分数对流扩散方程解中对偶伯恩斯坦算子的分析

Bernstein 算子 (BO) 不是正交的，但它们具有对偶，它们是通过 BO 的线性组合获得的。近年来，双 BO 已被用于计算机图形学、计算机辅助几何设计和数值分析。本文提出了一种基于 Bernstein 运算矩阵的数值方法来求解时空分数阶对流扩散方程。讨论了分数阶导数矩阵算子的推广和误差分析。数值例子将所提出的方法与以前的工作进行了比较，表明该方法更加准确和有效。