Abstract In this paper, we introduce the multi-variate spectral quasi-linearization method which is an extension of the previously reported bivariate spectral quasi-linearization method. The method is a combination of quasi-linearization techniques and the spectral collocation method to solve three-dimensional partial differential equations. We test its applicability on the (2 + 1) dimensional Burgers’ equations. We apply the spectral collocation method to discretize both space variables as well as the time variable. This results in high accuracy in both space and time. Numerical results are compared with known exact solutions as well as results from other papers to confirm the accuracy and efficiency of the method. The results show that the method produces highly accurate solutions and is very efficient for (2 + 1) dimensional PDEs. The efficiency is due to the fact that only few grid points are required to archive high accuracy. The results are portrayed in tables and graphs.

中文翻译：

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求解(2+1)维Burgers方程的一种多元谱拟线性化方法

摘要 在本文中，我们介绍了多变量谱拟线性化方法，它是先前报道的双变量谱拟线性化方法的扩展。该方法是将拟线性化技术与谱搭配法相结合来求解三维偏微分方程的方法。我们测试了它在 (2 + 1) 维 Burgers 方程上的适用性。我们应用光谱搭配方法来离散空间变量和时间变量。这导致空间和时间的高精度。将数值结果与已知精确解以及其他论文的结果进行比较，以确认该方法的准确性和效率。结果表明，该方法产生了高度准确的解，并且对于 (2 + 1) 维偏微分方程非常有效。效率是由于只需要很少的网格点即可实现高精度存档。结果用表格和图表表示。