一、简介和摘要 谱方法优于有限差分法,它没有相差,没有计算频散和混淆误差。直到1985年Tatsumi研究出单向套网格有限区域谱模式以后,谱方法才被应用到具有时变侧边界条件的有限区域模式中去。在有限区域模式中应用谱方法,问题在于怎样处理侧边界条件。作为特征函数的、从Sturm—Liouville的微分方程获得的标准谱基本函数满足特殊边界条件,但是不满足任意改变的边界条件。Tatsumi引进了修正付立叶级数和边界张弛法,从而成功地解决了 I. INTRODUCTION AND ABSTRACTION Spectral method is superior to finite difference method, it has no difference, does not calculate dispersion and confusion error. It was not until 1985 that Tatsumi developed a one-way nested grid finite-area spectral pattern that the spectral method was applied to the finite-area pattern with time-varying lateral boundary conditions. The problem with applying the spectral method in the finite area mode is how to deal with the side boundary conditions. As the eigenfunctions, the standard spectral basic functions obtained from the Sturm-Liouville differential equations satisfy the special boundary conditions but do not satisfy any changing boundary conditions. Tatsumi successfully introduced the modified Fourier series and the boundary relaxation method