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三阶微分方程的Legendre-Petrov-Galerkin谱元方法

DOI: 10.11830/ISSN.1000-5013.2013.03.0344

Keywords: 三阶微分方程, Legendre-Petrov-Gelarkin谱元法, 基函数, 线性系统, 数值实验

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Abstract:

针对建立在有限区间上的三阶微分方程,提出Legendre-Petrov- Galerkin谱元方法.通过构造满足试探函数空间和检验函数空间的基函数,得到离散问题所对应的稀疏的线性系统, 并对其进行求解. 数值例子验证了方法的有效性和高精度.

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