In this paper, we employ an efficient numerical method to solve transport equations with given boundary and initial conditions. By the weighted-orthogonal Chebyshev polynomials, we design the corresponding basis functions for spatial variables, which guarantee the stiff matrix is sparse, for the spectral collocation methods. Combining with direct algebraic algorithms for the sparse discretized formula, we solve the equivalent scheme to get the numerical solutions with high accuracy. This collocation methods can be used to solve other kinds of models with limited computational costs, especially for the nonlinear partial differential equations. Some numerical results are listed to illustrate the high accuracy of this numerical method.

中文翻译：

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求解输运方程的一种新的切比雪夫搭配谱方法

在本文中，我们采用一种有效的数值方法来求解具有给定边界和初始条件的输运方程。通过加权正交切比雪夫多项式，我们为光谱搭配方法设计了相应的空间变量基函数，保证了刚性矩阵的稀疏性。结合稀疏离散公式的直接代数算法，求解等价方案，得到高精度的数值解。这种搭配方法可用于求解其他类型的计算成本有限的模型，特别是对于非线性偏微分方程。列出了一些数值结果以说明该数值方法的高精度。