Stable and Efficient Spectral Methods in Unbounded Domains Using Laguerre Functions
Stable and Efficient Spectral Methods in Unbounded Domains Using Laguerre Functions
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DOI：
10.1137/s0036142999362936
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发表时间：
2000-09
期刊：
影响因子：
--
通讯作者：
Jie Shen
中科院分区：
文献类型：
--
作者：
Jie Shen
针对正则无界区域上的模型椭圆型方程，提出并分析了稳定有效的Laguerre函数谱方法。证明了在通常的Sobolev空间（不加权）中，基于Laguerre函数的谱Galerkin逼近是稳定的，且具有谱精度收敛性.高效，准确，良好的条件下使用Laguerre函数的算法的开发和实施。数值结果表明这些算法的谱收敛速度和有效性。
Stable and efficient spectral methods using Laguerre functions are proposed and analyzed for model elliptic equations on regular unbounded domains. It is shown that spectral-Galerkin approximations based on Laguerre functions are stable and convergent with spectral accuracy in the usual (not weighted) Sobolev spaces. Efficient, accurate, and well-conditioned algorithms using Laguerre functions are developed and implemented. Numerical results indicating the spectral convergence rate and effectiveness of these algorithms are presented.