Generalized Jacobi polynomials/functions and their applications
Generalized Jacobi polynomials/functions and their applications
复制标题
广义雅可比多项式/函数及其应用
DOI：
10.1016/j.apnum.2008.04.003
复制
发表时间：
2009-05-01
影响因子：
2.8
通讯作者：
Wang, Li-Lian
中科院分区：
文献类型：
--
作者：
Guo, Ben-Yu;Shen, Jie;Wang, Li-Lian
我们引入了一族广义Jacobi多项式/函数，其指标α，β是R的元素，它们关于相应的Jacobi权相互正交，并且继承了经典Jacobi多项式的某些重要性质。在适当加权的Sobolev空间中，我们建立了它们的基本逼近性质。作为应用的一个例子，我们证明了广义Jacobi多项式/函数，与指数对应的齐次边界条件的数量在一个给定的偏微分方程，是自然的基函数的谱近似的偏微分方程。此外，广义雅可比多项式/函数的使用导致更简化的分析，更精确的误差估计和良好的条件算法。(C)2008年IMACS。Elsevier B. V.出版，保留所有权利。
We introduce a family of generalized Jacobi polynomials/functions with indexes alpha, beta is an element of R which are mutually orthogonal with respect to the corresponding Jacobi weights and which inherit selected important properties of the classical Jacobi polynomials. We establish their basic approximation properties in suitably weighted Sobolev spaces. As an example of their applications, we show that the generalized Jacobi polynomials/functions, with indexes corresponding to the number of homogeneous boundary conditions in a given partial differential equation, are the natural basis functions for the spectral approximation of this partial differential equation. Moreover, the use of generalized Jacobi polynomials/functions leads to much simplified analysis, more precise error estimates and well conditioned algorithms. (C) 2008 IMACS. Published by Elsevier B.V. All rights reserved.