Introduction to spectral methods
Introduction to spectral methods
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DOI：
10.1051/eas:2006112
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发表时间：
2006-09
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影响因子：
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通讯作者：
P. Grandclément
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文献类型：
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作者：
P. Grandclément
这篇论文是谱方法的第一篇介绍。它是围绕一些简单的问题写的，这些问题得到了明确和详细的解决，目的是展示这些方法的力量。首先介绍了谱近似的数学基础，基于高斯求积。然后给出了勒让德多项式和切比雪夫多项式的两种常用基。下一节将专门介绍仅使用一个域的一维方程求解器。描述了三种不同的方法。在本文的最后一节中显示了使用几个域的技术，并讨论了它们的各种优点。
This proceeding is intended to be a first introduction to spectral methods. It is written around some simple problems that are solved explicitly and in details and that aim at demonstrating the power of those methods. The mathematical foundation of the spectral approximation is first introduced, based on the Gauss quadratures. The two usual basis of Legendre and Chebyshev polynomials are then presented. The next section is devoted to one dimensional equation solvers using only one domain. Three different methods are described. Techniques using several domains are shown in the last section of this paper and their various merits discussed.