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：iii。线性微分方程具有恒定系数的傅立叶系列多尺度方法
Fourier series (based) multiscale method for computational analysis in science and engineering: III. Fourier series multiscale method for linear differential equation with constant coefficients
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。在第三篇论文中，解决了具有恒定系数并遵循一般边界条件的2r-tord线性微分方程固有的多尺度现象的分析分析。首先讨论了基于代数多项式插值的局限性。这导致了复合傅立叶系列方法的新公式，其中采用微分方程的均匀解作为插值函数。因此，提供了傅立叶级数多尺度方法的理论框架，其中指定了微分方程解决方案的分解结构，并详细介绍了用于应用程序的实施方案。傅立叶系列多尺度方法不仅充分利用了傅立叶系列方法的现有成就，而且对微分方程解决方案解决方案的结构分解的基本位置也显着，从而使傅立叶系列解决方案的一致性和灵活性完美整合。
Fourier series multiscale method, a concise and efficient analytical approach for multiscale computation, will be developed out of this series of papers. In the third paper, the analytical analysis of multiscale phenomena inherent in the 2r-th order linear differential equations with constant coefficients and subjected to general boundary conditions is addressed. The limitation of the algebraical polynomial interpolation based composite Fourier series method is first discussed. This leads to a new formulation of the composite Fourier series method, where homogeneous solutions of the differential equations are adopted as interpolation functions. Consequently, the theoretical framework of the Fourier series multiscale method is provided, in which decomposition structures of solutions of the differential equations are specified and implementation schemes for application are detailed. The Fourier series multiscale method has not only made full use of existing achievements of the Fourier series method, but also given prominence to the fundamental position of structural decomposition of solutions of the differential equations, which results in perfect integration of consistency and flexibility of the Fourier series solution.
