变系数2D对流扩散方程的高阶迭代算子分裂方法
Higher Order Iterative Operator Splitting Method for the 2D Convection Diffusion Equation with Variable Coefficients
DOI: 10.12677/AAM.2017.63030, PDF, HTML, XML, 下载: 1,835  浏览: 4,339  国家自然科学基金支持
作者: 姚林, 苏海燕：新疆大学数学与系统科学学院，新疆 乌鲁木齐
关键词: 对流扩散；Zassenhaus乘积；高阶迭代；傅立叶拟谱；Convection Diffusion； Zassenhaus Product； Higher Order Iterative； Fourier Pseudo Spectral
摘要: 本文针对变系数2D对流扩散方程，呈现了一种新颖的高阶迭代算子分裂方法。该方法结合了经典迭代格式和Zassenhaus乘积公式。傅立叶谱方法和维数分裂格式用于空间算子。数值实验验证了所提出的方法通过加权方法可以达到高阶精度。此外，新方法不仅可以减少误差而且能够节省大量的CPU时间。
Abstract: In this paper, a novel higher order iterative operator splitting method is presented for the 2D convection diffusion equation with the variable coefficient. The proposed scheme combines the classical iterative scheme and Zassenhaus product formula for the temporal discretization. And Fourier pseudo spectral method and dimensional splitting scheme are applied for the spatial operators. The numerical results verified that the proposed method can get second order accuracy by weighted iterative scheme. Besides, the new method not only can reduce numerical error but also save a lot of CPU time than the classical iterative method.
文章引用：姚林, 苏海燕. 变系数2D对流扩散方程的高阶迭代算子分裂方法[J]. 应用数学进展, 2017, 6(3): 249-258. https://doi.org/10.12677/AAM.2017.63030

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