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半无界条状区域四阶方程的Laguerre-Legendre混合谱逼近

DOI: 10.11830/ISSN.1000-5013.2013.04.0471

Keywords: 四阶方程, 半无界条状区域, Laguerre-Legendre混合谱, 基函数, 收敛性

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Abstract:

对二维半无界条状区域上的四阶偏微分方程,用不带权函数的Laguerre-Legendre混合谱方法进行逼近.通过构造满足微分方程边界条件的基函数,由离散变分公式可以得到具有稀疏系数矩阵的代数系统,从而有效地进行求解.对该方法进行严格的收敛性分析,数值结果验证了方法的收敛性和有效性.

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