论文标题
傅立叶系列（基于）科学与工程中计算分析的多尺度方法：IV。傅立叶系列多尺度解决方案用于对流扩散反应方程
Fourier series (based) multiscale method for computational analysis in science and engineering: IV. Fourier series multiscale solution for the convection-diffusion-reaction equation
论文作者
论文摘要
傅立叶系列多尺度方法是一种简洁有效的多尺度计算方法，将根据这一系列论文开发。在第四篇论文中，实施了傅立叶系列多尺度方法在一维对流扩散反应方程式中的应用，其中得出了傅立叶级数多尺度解决方案，傅立叶串联多尺度解决方案的收敛特征是通过数值示例进行的，用于数值的实例，以求缩式多层尺度的速度化的跨度尺度，并在远方级数。证明了方程式。对应用的初步研究验证了当前傅立叶系列多尺度方法的有效性，并提供了可靠的参考，可用于持续改善其他多尺度方法的计算性能。
Fourier series multiscale method, a concise and efficient analytical approach for multiscale computation, will be developed out of this series of papers. In the fourth paper, the application of the Fourier series multiscale method to the one- and two-dimensional convection-diffusion-reaction equations is implemented, where the Fourier series multiscale solutions are derived, the convergence characteristics of the Fourier series multiscale solutions are investigated by numerical examples, the schemes for application of the Fourier series multiscale method are optimized, and the multiscale characteristics of the convection-diffusion-reaction equations are demonstrated. The preliminary study on applications verifies the effectiveness of the present Fourier series multiscale method and provides a reliable reference which can be used for persistent improvement in computational performance of other multiscale methods.
